[{"data":1,"prerenderedAt":23},["ShallowReactive",2],{"formula-en-hertz-pressure-distribution":3},{"formula":4,"related_topics":12,"alternates":20},{"id":5,"code":6,"slug":6,"title":7,"formula":8,"locale":9,"seo_title":10,"seo_description":10,"content_html":11},126,"hertz-pressure-distribution","Hertz Contact Pressure Distribution","p₀ = 3F \u002F (2πa²)","en",null,"\u003Cdiv class=\"formula-chunk\">\u003Cp>For a circular Hertz contact area of radius $a$, the pressure varies as:\u003C\u002Fp>\u003Cp>$$p(r)=p_0\\sqrt{1-\\frac{r^2}{a^2}},\\qquad 0\\le r\\le a.$$\u003C\u002Fp>\u003Cp>The maximum pressure at the center is:\u003C\u002Fp>\u003Cp>$$p_0=\\frac{3F}{2\\pi a^2}.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$p(r)$\u003C\u002Fstrong> — contact pressure at distance $r$ from the center;\u003C\u002Fli>\u003Cli>\u003Cstrong>$p_0$\u003C\u002Fstrong> — maximum contact pressure;\u003C\u002Fli>\u003Cli>\u003Cstrong>$a$\u003C\u002Fstrong> — contact radius;\u003C\u002Fli>\u003Cli>\u003Cstrong>$r$\u003C\u002Fstrong> — radial coordinate within the contact patch;\u003C\u002Fli>\u003Cli>\u003Cstrong>$F$\u003C\u002Fstrong> — normal force.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>At the contact boundary $p(a)=0$, while the maximum $p_0$ occurs at $r=0$.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>\u003C\u002Fdiv>",[13,16],{"id":5,"name":14,"path":15},"Contact Stresses","strength-of-materials\u002Fcontact-stresses",{"id":17,"name":18,"path":19},128,"Hertz Theory: Main Assumptions and Formulas","strength-of-materials\u002Fcontact-stresses\u002Fhertz-contact-theory",{"en":21,"uk":22},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Fformulas\u002Fhertz-pressure-distribution","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Fhertz-pressure-distribution",1787712544173]