CONTACT軟件基于著名計(jì)算力學(xué)專(zhuān)家、荷蘭代爾夫特理工大學(xué)J. J. Kalker教授的三維滾動(dòng)接觸理論（卡爾克理論）開(kāi)發(fā)而成?？柨死碚撟钤缭谖墨I(xiàn)[14]中提出，而后在文獻(xiàn)[17]中詳細(xì)闡述，文獻(xiàn)[19]和[51]分別有一些擴(kuò)展的描述。Edwin Vollebregt博士在其導(dǎo)師J. J. Kalker教授的基礎(chǔ)上，進(jìn)一步研發(fā)和拓展，增加了自動(dòng)輪軌幾何接觸分析[49, 50]、考慮第三層介質(zhì)效應(yīng)[44, 56]和負(fù)斜率特性[53]等功能，采用全新的迭代求解器提高了求解效率[43, 63]，現(xiàn)在的程序可稱作“Extended CONTACT”。Extended CONTACT是一款用于精細(xì)化三維摩擦接觸分析的高級(jí)仿真軟件，主要應(yīng)用于精確的輪軌蠕滑力特性研究，進(jìn)而可支持輪軌型面磨耗和滾動(dòng)接觸疲勞分析[24, 25]。

CONTACT的使用方式

CONTACT軟件支持以不同的方式運(yùn)行：

• CONTACT Stand-alone version：定義具體的一個(gè)或幾個(gè)關(guān)聯(lián)工況參數(shù)，獲得完整的計(jì)算結(jié)果，使用MATLAB繪圖子程序進(jìn)行后處理；

• USETAB：求解大量的關(guān)聯(lián)工況，將獲得的計(jì)算結(jié)果制作成數(shù)表用于其他商業(yè)軟件或自編程序；

• CONTACT Libraries：通過(guò)第三方軟件以動(dòng)態(tài)鏈接庫(kù)（DLL）的形式調(diào)用CONTACT的求解內(nèi)核（完全集成），提供MATLAB、Fortran和C等程序語(yǔ)言接口。

第一種方式是CONTACT軟件最基本的運(yùn)行方式，后面兩種方式主要用在車(chē)輛系統(tǒng)動(dòng)力學(xué)（VSD）軟件的磨耗計(jì)算。目前，商業(yè)軟件Universal Mechanism（完全集成）、GENSYS（完全集成）、NUCARS（數(shù)表形式）、SIMPACK?Rail[57]與CONTACT已經(jīng)實(shí)現(xiàn)了不同程度的協(xié)作。

CONTACT的用戶手冊(cè)

本文內(nèi)容翻譯自用戶手冊(cè)第一章，其他章節(jié)主要內(nèi)容如下：

• 第二章簡(jiǎn)略地介紹了接觸計(jì)算的理論模型，以滿足軟件操作的最低要求，更詳細(xì)的內(nèi)容和參考資料請(qǐng)查閱文獻(xiàn)[17, 19, 51]；

• 第三章介紹了軟件的基本操作，包括命令行和界面操作、有關(guān)模塊和工況的術(shù)語(yǔ)以及操縱程序的控制符；

• 第四章介紹輪軌接觸分析（一號(hào)模塊）詳細(xì)的輸入量和輸出量；

• 第五章介紹通用的赫茲和非赫茲接觸分析（三號(hào)模塊）詳細(xì)的輸入量和輸出量；

• 第六章通過(guò)一些具體的例子演示CONTACT獨(dú)立版本的使用方法；

• 第七章介紹使用MATLAB腳本進(jìn)行后處理可視化操作；

• 第八章介紹CONTACT動(dòng)態(tài)鏈接庫(kù)的用法；

• 最后，附錄A詳細(xì)描述了計(jì)算輸入文件的格式和邏輯選項(xiàng)。

初學(xué)者導(dǎo)航

眾所周知，CONTACT并不是一個(gè)很容易掌握的簡(jiǎn)單軟件。

• 首先，最主要的原因是完整全面地介紹接觸力學(xué)的書(shū)籍并不多見(jiàn)，雖然Johnson[11]和Kalker[17]的著作非常經(jīng)典，但要熟悉這些理論和知識(shí)本身也是一種挑戰(zhàn)，這對(duì)數(shù)學(xué)基礎(chǔ)要求很高。作者更推薦Popov[30]的著作，書(shū)中對(duì)接觸現(xiàn)象有更通俗的介紹。此外，文獻(xiàn)[55]是關(guān)于輪軌蠕滑模型的綜述，對(duì)于輪軌接觸領(lǐng)域的研究人員非常有用。

• 其次，軟件本身要兼容各種各樣的工況，這對(duì)簡(jiǎn)單工作流程和簡(jiǎn)單繪圖程序的開(kāi)發(fā)造成了阻礙。

• 最后，軟件至今保留著古老的輸入文件結(jié)構(gòu)，其中包含許多控制符和邏輯選項(xiàng)。

其實(shí)，在我們看來(lái)，如果用戶知道接觸力學(xué)的基本概念和術(shù)語(yǔ)，那么操作CONTACT軟件并非難事。為了快速熟悉輸入文件的內(nèi)容和格式，建議如下操作：

1. 請(qǐng)將CONTACT用戶手冊(cè)通讀一遍，重點(diǎn)（反復(fù)）閱讀第三、四和五章。

2. 參照用戶手冊(cè)第六章的描述，運(yùn)行軟件自帶的算例。

3. 在用戶手冊(cè)第3.3章節(jié)和附錄A.2放置書(shū)簽，因?yàn)榭刂品瓦壿嬤x項(xiàng)是需要經(jīng)常查閱的。

參考文獻(xiàn)

1. R.H. Bentall and K.L. Johnson. Slip in the rolling contact of two dissimilar elastic rollers.?Int.J. of Mechanical Sciences, 9:380–404, 1967.

2. J. Blanco-Lorenzo, J. Santamaria, E.G. Vadillo, and N. Correa. On the influence of conformity on wheel-rail rolling contact mechanics.?Tribology International, 103:647–667, 2016.

3. J. Blanco-Lorenzo, E.A.H. Vollebregt, J. Santamaria, and E.G. Vadillo. Approximating the influence coefficients of non-planar elastic solids for conformal contact analysis.?Tribology International, 154:106671, 2021.

4. A.F. Bower.?Applied Mechanics of Solids. CRC Press, Taylor and Francis Group, Boca Raton, 2010. See www.solidmechanics.org.

5. R.R. Craig Jr. and A.J. Kurdila.?Fundamentals of structural dynamics, 2nd edition. John Wiley & Sons, Hoboken, New Jersey, 2006.

6. B.E. Croft, E.A.H. Vollebregt, and D.J. Thompson. An investigation of velocity-dependent friction in wheel-rail rolling contact. In M. Uchida, T. Maeda, and K. Goto, editors,?Proceedings of the 10th International Workshop on Railway Noise, Nagahama, Japan, 2010.

7. B. Engel, H.P. Beck, and J. Alders. Verschlei?reduzierende Radschlupfregelung mit hoher Kraftschlussausnutzung.?Elektrische Bahnen, 96:201–209, 1998.

8. M. Ertz and K. Knothe. A comparison of analytical and numerical methods for the calculation of temperatures in wheel/rail contact.?Wear, 253:498–508, 2002.

9. R.C. Hibbeler.?Engineering Mechanics - Statics and Dynamics, 13th Edition. Pearson Prentice Hall, Upper Saddle River, New Jersey, 2012.

10. K. Hou, J. Kalousek, and E. Magel. Rheological model of solid layer in rolling contact.?Wear, 211:134–140, 1997.

11. K.L. Johnson.?Contact Mechanics. Cambridge University Press, Cambridge (UK), 1985.

12. J.J. Kalker.?On the rolling contact of two elastic bodies in the presence of dry friction. PhD thesis, Delft University of Technology, 1967.

13. J.J. Kalker. Simplified theory of rolling contact.?Delft Progress Report Series C1, 1:1–10, 1973.

14. J.J. Kalker. The computation of three-dimensional rolling contact with dry friction.?Int. Journ. for Numerical Methods in Engineering, 14:1293–1307, 1979.

15. J.J. Kalker. A fast algorithm for the simplified theory of rolling contact.?Vehicle System Dynamics, 11:1–13, 1982.

16. J.J. Kalker. Numerical calculation of the elastic field in a half-space.?Comm. Appl. Num. Meth., 2:401–410, 1986. Reprinted as Appendix C in [17].

17. J.J. Kalker.?Three-Dimensional Elastic Bodies in Rolling Contact, volume 2 of?Solid Mechanics and its Applications. Kluwer Academic Publishers, Dordrecht, Netherlands, 1990.

18. J.J. Kalker. Book of tables for the Hertzian creep-force law. In Zobory [64], pages 11–20.

19. J.J. Kalker. Rolling contact phenomena - linear elasticity. In B. Jacobson and J.J. Kalker, editors,?Rolling Contact Phenomena, volume 411 of?CISM Courses and Lectures, pages 1–85. Springer-Verlag, Wien New York, 2000.

20. J.J. Kalker, F.M. Dekking, and E.A.H. Vollebregt. Simulation of rough, elastic contacts.?Journal of Applied Mechanics, 64(2):361–368, 1997.

21. Zili Li.?Wheel-rail rolling contact and its application to wear simulation. PhD thesis, Delft University of Technology, 2002.

22. A.E.H. Love. Stress produced in a semi-infinite solid by pressure on part of the boundary.?Philosophical Transactions of the Royal Society of London, A228:377–420, 1929.

23. M. Malvezzi, E. Meli, S. Falomi, and A. Rindi. Determination of wheel-rail contact points with semianalytic methods.?Multibody System Dynamics, 20:327–358, 2008.

24. S.Z. Meymand, A. Keylin, and M. Ahmadian. A survey of wheel-rail contact models for rail vehicles.?Vehicle System Dynamics, 54:368–428, 2016.

25. R. Munisamy, D.A. Hills, and D. Nowell. Brief note on the tractive rolling of dissimilar elastic cylinders.?Int. Journ. of Mechanical Sciences, 33(3):225–228, 1991.

26. P.M. Naghdi.?P.M. Naghdi’s Notes on Continuum Mechanics. University of California, Department of Mechanical Engineering, Berkeley, 2001.

27. J.B. Nielsen and A. Theiler. Tangential contact problem with friction coefficients depending on sliding velocity. In Zobory [64], pages 44–51.

28. J. Piotrowski, B.B. Liu, and S. Bruni. The Kalker book of tables for non-Hertzian contact of wheel and rail.?Vehicle System Dynamics, 55:875–901, 2017. DOI: 10.1080/00423114.2017.1291980.

29. O. Polach. Creep forces in simulations of traction vehicles running on adhesion limit.?Wear, 258:992–1000, 2005.

30. V.L. Popov.?Contact Mechanics and Friction. Physical Principles and Applications. SpringerVerlag, Berlin, 2010.

31. D. Roylance. Engineering viscoelasticity. Technical report, Massachusetts Institute of Technology, Cambridge, MA, USA, 2001.

32. A.A. Shabana.?Dynamics of Multibody Systems – Fourth Edition. Cambridge University Press, New York, 2013.

33. A.A. Shabana, K.E. Zaazaa, and H. Sugiyama.?Railroad Vehicle Dynamics: A Computational Approach. CRC Press, Boca Raton, 2008.

34. P. Shackleton and S.D. Iwnicki. Wheel-rail contact benchmark, version 3.0. Rail Technology Unit, Manchester Metropolitan University, 2006.

35. P. Shackleton and S.D. Iwnicki. Comparison of wheel-rail contact codes for railway vehicle simulation: an introduction to the Manchester Contact Benchmark and initial results.?Vehicle System Dynamics, 46(1-2):129–149, 2008.

36. M. Spiryagin, O. Polach, and C. Cole. Creep force modelling for rail traction vehicles based on the Fastsim algorithm.?Vehicle System Dynamics, 51:1765–1783, 2013.

37. A.S.K.S. Tjoeng and J.J. Kalker. User’s manual for the program DUVOROL in Algol 60 & Fortran for the computation of three-dimensional rolling contact with dry friction. Technical report, Delft University of Technology, Delft, June 1980.

38. E.A.H. Vollebregt. A Gauss-Seidel type solver for special convex programs, with application to frictional contact mechanics.?J. of Optimization Theory and Applications, 87(1):47–67, 1995.

39. E.A.H. Vollebregt. Refinement of Kalker’s rolling contact model. In A. Bracciali, editor,?Proceedingsofthe8thInternationalConferenceonContactMechanicsandWearofRail/Wheel Systems, pages 149–156, Firenze, Italy, 2009. University of Firenze.

40. E.A.H. Vollebregt. User guide for CONTACT, J.J. Kalker’s variational contact model. Technical Report TR09-03, v9.1, VORtech, 2009.

41. E.A.H. Vollebregt. Improving the speed and accuracy of the frictional rolling contact model “CONTACT”. In B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, and M.L. Romero, editors,?Proceedings of the 10th International Conference on Computational Structures Technology, pages 1–15, Stirlingshire, United Kingdom, 2010. Civil-Comp Press. DOI: 10.4203/ccp.93.17.

42. E.A.H. Vollebregt. The Bound-Constrained Conjugate Gradients method for non-negative matrices.?J. of Optimization Theory and Applications, 162(3):931–953, 2014. DOI: 10.1007/s10957-013-0499-x.

43. E.A.H. Vollebregt. A new solver for the elastic normal contact problem using conjugate gradients, deflation, and an FFT-based preconditioner.?J. of Computational Physics, 257, Part A:333–351, 2014.

44. E.A.H. Vollebregt. Numerical modeling of measured railway creep versus creep-force curves with CONTACT.?Wear, 314:87–95, 2014.

45. E.A.H. Vollebregt. New insights in non-steady rolling contact. In M. Rosenberger, editor,?Proceedings of the 24th International Symposium on Dynamics of Vehicles on Roads and Tracks, Graz, Austria, 2015. IAVSD.

46. E.A.H. Vollebregt. Updates on the rocking phenomenon. In M. Spiryagin, T. Gordon, C. Cole, and T. McSweeney, editors,?Proceedings of the 25th International Symposium on Dynamics of Vehicles on Roads and Tracks, pages 605–611, Rockhampton, Queensland, Australia, 2017. IAVSD.

47. E.A.H. Vollebregt. Comments on “the Kalker book of tables for non-Hertzian contact of wheel and rail”.?Vehicle System Dynamics, 56(9):1451–1459, 2018. DOI: 10.1080/00423114.2017.1421767.

48. E.A.H. Vollebregt. Conformal contact: Corrections and new results.?Vehicle System Dynamics, 56(10):1622–1632, 2018. DOI: 10.1080/00423114.2018.1424917.

49. E.A.H. Vollebregt. Detailed wheel/rail geometry processing using the planar contact approach.?Vehicle System Dynamics, 2020. DOI: 10.1080/00423114.2020.1853180, open access.

50. E.A.H. Vollebregt. Detailed wheel/rail geometry processing using the conformal contact approach.?Multibody System Dynamics, 52:135–167, 2021. Open access.

51. E.A.H. Vollebregt, S.D. Iwnicki, G. Xie, and P. Shackleton. Assessing the accuracy of different simplified frictional rolling contact algorithms.?Vehicle System Dynamics, 50(1):1–17, 2012. DOI: 10.1080/00423114.2011.552618.

52. E.A.H. Vollebregt, J.J. Kalker, and G.Q. Wang. CONTACT’93 users manual. Technical report, Delft University of Technology, 1993.

53. E.A.H.VollebregtandH.M.Schuttelaars. Quasi-staticanalysisof2-dimensionalrollingcontact with slip-velocity dependent friction.?J. of Sound and Vibration, 331(9):2141–2155, 2012. DOI: 10.1016/j.jsv.2012.01.011.

54. E.A.H.VollebregtandA.Segal. Solvingconformalwheel-railrollingcontactproblems.?Vehicle System Dynamics, 52(suppl. 1):455–468, 2014. DOI: 10.1080/00423114.2014.906634.

55. E.A.H. Vollebregt, K. Six, and O. Polach. Challenges and progress in the understanding and modelling of the wheel–rail creep forces.?Vehicle System Dynamics, 59(7):1026–1068, 2021.

56. E.A.H. Vollebregt and C.D. van der Wekken. Advanced modeling of wheel-rail friction phenomena. Technical Report TR19-11, VORtech, November 2019. FRA project.

57. E.A.H. Vollebregt, C. Weidemann, and A. Kienberger. Use of “CONTACT” in multi-body vehicle dynamics and profile wear simulation: Initial results. In S.D. Iwnicki, editor,?Proceedings of the 22nd International Symposium on Dynamics of Vehicles on Roads and Tracks, pages 1–6, Manchester, 2011. IAVSD.

58. E.A.H.VollebregtandP.Wilders. FASTSIM2: asecondorderaccuratefrictionalrollingcontact algorithm.?Comput.Mech., 47(1):105–116, 2010. DOI: 10.1007/s00466-010-0536-7, open access.

59. G. Wang and J.J. Kalker. Three-dimensional rolling contact of two viscoelastic bodies. In A. Curnier, editor,?Contact Mechanics. Proceedings; International Symposium, October 7 - 9, 1992, Ecole Polytechnique Fédérale de Lausanne, pages 477–490, Lausanne, 1992. Presses Polytechniques et Universitaires Romandes.

60. G. Wang and K. Knothe. Stress analysis for rolling contact between two viscoelastic cylinders.?Journal of Applied Mechanics; Transactions ASME, 60:310–317, 1993.

61. C.D. van der Wekken and E.A.H. Vollebregt. Numerical calculation of the elastic field in a half-space using bilinear elements.?Mathematics and Mechanics of Solids, 24(11):3537–3553, 2019.

62. C.D. van der Wekken, E.A.H. Vollebregt, and C. Vuik. Occurrence and removal of wiggles in transient rolling contact simulation. In J. Ambrósio, W. Schielen, and J. Pombo, editors,?Proceedings of EuroMech colloquim 578 on Rolling Contact Mechanics for Multibody System Dynamics, pages 1–11, Lisbon, Portugal, 2017. IDMEC.

63. J. Zhao, E.A.H. Vollebregt, and C.W. Oosterlee. A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems.?J. of Computational Physics, 288:86– 100, 2015.

64. I. Zobory, editor.?Proceedings of the 2nd Mini Conference on Contact mechanics and Wear of Wheel/Rail systems. Technical University of Budapest, Hungary, 1996.