Variable speed steering system has been used by cars of various brands, including BMW and Toyota, with the purpose of improving the stationarity and controllability of the vehicle. Until now, relevant investigations are focused on the theory and traditional application, while the geometric characteristics and tooth modification for the rack are left untouched upon, hindering the prospect of a wider application. Focusing on this, the paper synthesizes the mathematical model, geometry characteristics, and tooth modification method for the variable pinion–rack drive. The major contributions lie in the contact analysis and the modification methodology for the pinion–rack drive, which combined forms a solid foundation for the application that has never been discussed.
ZhaoWZhangHLiY. Displacement and force coupling control design for automotive active front steering system. Mech Syst Signal Process2018; 106: 76–93.
2.
VerlAEngelberthT. Adaptive preloading for rack-and-pinion drive systems. CIRP Ann – Manuf Technol2018; 67: 369–372.
3.
LitvinF-AGonzalez-PerezH. Noncircular gears: design and generation, Cambridge: Cambridge University Press, 2015.
4.
DoonerDB. Kinematic geometry of gearing, Chichester, UK: Wiley, Ltd., 2012.
5.
DoegeEHindersmannM. Optimized kinematics of mechanical presses with noncircular gears. CIRP Ann1997; 46: 213–216.
6.
DoonerDB. Use of noncircular gears to reduce torque and speed fluctuations in rotating shafts. Trans ASME J Mech Des1997; 119: 299–306.
7.
DoonerDB. Function generation utilizing an eight-link mechanism and optimized non-circular gear elements with application to automotive steering. Proc IMechE, Part C: J Mechanical Engineering Science2001; 215: 847–857.
8.
MundoDGattiGDoonerDB. Optimized five-bar linkages with non-circular gears for exact path generation. Mech Mach Theory2009; 44: 751–760.
9.
MundoD. Geometric design of a planetary gear train with non-circular gears. Mech Mach Theory2006; 41: 456–472.
10.
OttavianoEMundoDDanieliGA, et al.Numerical and experimental analysis of non-circular gears and cam-follower systems as function generators. Mech Mach Theory2008; 43: 996–1008.
11.
ModlerK-HLovaszE-CBärGF, et al.General method for the synthesis of geared linkages with non-circular gears. Mech Mach Theory2009; 44: 726–738.
12.
KarpovONoskoPFilP, et al.Prevention of resonance oscillations in gear mechanisms using non-circular gears. Mech Mach Theory2017; 114: 1–10.
13.
AddomineMFiglioliniGPennestrìE. A landmark in the history of non-circular gears design: The mechanical masterpiece of Dondi’s astrarium. Mech Mach Theory2018; 122: 219–232.
14.
ZhengFHuaLHanX. The mathematical model and mechanical properties of variable center distance gears based on screw theory. Mech Mach Theory2016; 101: 116–139.
15.
ZhengFHuaLHanX, et al.Synthesis of indexing mechanisms with non-circular gears. Mech Mach Theory2016; 105: 108–128.
16.
EmuraTArakawaA. A new steering mechanism using noncircular gears. JSME Int J1992; 35: 604–610.
17.
LitvinFLGonzalez-PerezIFuentesA, et al.Design and investigation of gear drives with non-circular gear applied for speed variation and generation of functions. Comput Methods Appl Mech Eng2008; 197: 3783–3802.
18.
BendefyAGPirosAHorákP. Arbitrary vehicle steering characteristics with changing ratio rack and pinion transmission. Adv Mech Eng2015; 7: 168781401561927–168781401561927.
19.
AlexandruPMacaveiuDAlexandruC. A gear with translational wheel for a variable transmission ratio and applications to steering box. Mech Mach Theory2012; 52: 267–276.
20.
Alexandru P, Ceausescu B and Diaconescu D. Importants aspects of geometry of the pinion-rack gear with variable ratio. In: Proceedings of the 8th IFToMM international symposium on science of mechanisms and machines – SYROM, Bucharest, vol. III, 2001, pp.13–18.
21.
Adams FJ. Pinion for variable ratio rack and pinion steering gear. U.S. Patent 3983763[P], 1976-10-5, 1976.
22.
Higuchi M. Variable ratio rack and pinion steering gear. U.S. Patent 4475413[P], 1984-10-9, 1984.
23.
Yanai T. Variable ratio rack and pinion steering gear. U.S. Patent 4444070[P], 1984-4-24, 1984.
24.
FiglioliniGAngelesJ. The synthesis of elliptical gears generated by shaper-cutters. ASME J Mech Des2003; 125: 793–801.
25.
Shimizu Y, Kawai T and Yuzuriha J. Improvement in driver-vehicle system performance by varying steering gain with vehicle speed and steering angle: VGS (variable gear-ratio steering system). SAE Technical Paper 1999-01-0395, 1999.
26.
ZhangNWangM. Dynamic modeling of hydraulic power steering system with variable ratio rack and pinion gear. JSME Int J2005; 48: 251–260.
27.
ZhengFYZhangMDZhangWQ, et al.On the deformed tooth contact analysis for forged bevel gear modification. Mech Mach Theory2019; 135: 192–207.
28.
FuentesARuiz-OrzaezRGonzalez-PerezI. Computerized design, simulation of meshing, and finite element analysis of two types of geometry of curvilinear cylindrical gears. Comput Methods Appl Mech Eng2014; 272: 321–339.
29.
SimonVV. Influence of tooth modifications on tooth contact in face-hobbed spiral bevel gears. Mech Mach Theory2011; 46: 1980–1998.
30.
Zhou Y, Wang S, Wang L, et al, CNC milling of face gears with a novel geometric analysis. Mech Mach Theory 2019; 139: 46–65.
31.
FongZ-HChenG-H. Gear flank modification using a variable lead grinding worm method on a computer numerical control gear grinding machine. J Mech Des2016; 138: 083302–083302.
32.
DingHTangJYZhongJ. Accurate nonlinear modeling and computing of grinding machine settings modification considering spatial geometric errors for hypoid gears. Mech Mach Theory2016; 99: 155–175.
33.
ZschippangHAWeikertSKüçükKA, et al.Face-gear drive: geometry generation and tooth contact analysis. Mech Mach Theory2019; 142: 103576–103576.
34.
ZhengFYHuaLHanXH, et al.Synthesis of shaped noncircular gear using a three-linkage computer numerical control shaping machine. J Manuf Sci Eng2017; 139: 071003–071003-12.
35.
ZhengFYZhangMDZhangWQ, et al.Research on the tooth modification in gear skiving. J Mech Des ASME2018; 140: 084502–084502.
36.
LinCHeCJHuY. Analysis on the kinematical characteristics of compound motion curve-face gear pair. Mech Mach Theory2018; 128: 298–313.
37.
LiuDWWangGHRenTZ. Transmission principle and geometrical model of eccentric face gear. Mech Mach Theory2017; 109: 51–64.
38.
FuentesAIserteJLGonzalez-PerezI, et al.Computerized design of advanced straight and skew bevel gears produced by precision forging. Comput Methods Appl Mech Eng2011; 200: 2363–2377.
39.
DanielliGAMundoD. New developments in variable radius gear using constant pressure angle teeth. Mech Mach Theory2005; 40: 203–217.
40.
ZhengFYHuaLHanXH, et al.Generation of noncircular bevel gears with free-form tooth profile and tooth length based on screw theory. ASME J Mech Des2016.
41.
ZhengFYHuaLHanXH, et al.Linkage model and manufacturing process of shaping non-circular gears. Mech Mach Theory2016; 96: 192–212.
42.
WangPZhangYWanM. Third order curvature analysis of conjugate surfaces. Mech Mach Theory2017; 107: 87–104.
43.
KolivandMKahramanA. A load distribution model for hypoid gears using ease-off topography and shell theory. Mech Mach Theory2009; 44: 1848–1865.
44.
Zhou Y, Wu Y, Wang L. Tang H. Ouyang A. A new closed-form calculation of envelope surface for modeling face gears. Mech Mach Theory 2019; 137: 211–226.
45.
LitvinFLFuentesA. Gear geometry and applied theory, Cambridge: Cambridge University Press, 2004.
46.
ZhengFYHanXGHuaL, et al.Design and manufacture of new type of non-circular cylindrical gear generated by face-milling method. Mech Mach Theory2018; 122: 326–346.
