[{"data":1,"prerenderedAt":36},["ShallowReactive",2],{"formula-en-hertz-reduced-radius":3},{"formula":4,"related_topics":12,"alternates":33},{"id":5,"code":6,"slug":6,"title":7,"formula":8,"locale":9,"seo_title":10,"seo_description":10,"content_html":11},125,"hertz-reduced-radius","Reduced Radius of Curvature in Hertz Contact","1\u002FR* = 1\u002FR1 + 1\u002FR2","en",null,"\u003Cdiv class=\"formula-chunk\">\u003Cp>For two convex spherical surfaces along a corresponding principal direction, the reduced radius can be written as:\u003C\u002Fp>\u003Cp>$$\\frac{1}{R^*}=\\frac{1}{R_1}+\\frac{1}{R_2}.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$R^*$\u003C\u002Fstrong> — reduced radius of curvature;\u003C\u002Fli>\u003Cli>\u003Cstrong>$R_1$, $R_2$\u003C\u002Fstrong> — radii of curvature of the contacting surfaces.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>Equivalently, for two convex surfaces:\u003C\u002Fp>\u003Cp>$$R^*=\\frac{R_1R_2}{R_1+R_2}.$$\u003C\u002Fp>\u003Cp>For other combinations of curvature, the sign of an individual radius follows the adopted geometric convention. General three-dimensional contact requires the principal curvatures of both surfaces.\u003C\u002Fp>\u003Cp>The calculator below corresponds to two convex surfaces with positive radii.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>\u003C\u002Fdiv>",[13,17,21,25,29],{"id":14,"name":15,"path":16},127,"Contact of Two Bodies: Types and Geometry","strength-of-materials\u002Fcontact-stresses\u002Fcontact-types-and-geometry",{"id":18,"name":19,"path":20},126,"Contact Stresses","strength-of-materials\u002Fcontact-stresses",{"id":22,"name":23,"path":24},128,"Hertz Theory: Main Assumptions and Formulas","strength-of-materials\u002Fcontact-stresses\u002Fhertz-contact-theory",{"id":26,"name":27,"path":28},129,"Contact of Spheres and Spherical Surfaces","strength-of-materials\u002Fcontact-stresses\u002Fcontact-of-spheres-and-spherical-surfaces",{"id":30,"name":31,"path":32},130,"Contact of Cylinders and Rollers","strength-of-materials\u002Fcontact-stresses\u002Fcontact-of-cylinders-and-rollers",{"en":34,"uk":35},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Fformulas\u002Fhertz-reduced-radius","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Fhertz-reduced-radius",1787712544152]