Budynas-Nisbett:Shigley's Ill.Design of Mechanical 14.Spur and Helical Gears T©The McGraw-Hill m Mechanical Engineering Elements Companies,2008 Design,Eighth Edition Spur and Helical Gears 719 In the nineteenth century,Carl G.Barth first expressed the velocity factor,and in terms of the current AGMA standards,they are represented as 600+V K= (cast iron,cast profile) (14-4a 600 1200+V K= (cut or milled profile) (14-46) 1200 where V is the pitch-line velocity in feet per minute.It is also quite probable,because of the date that the tests were made,that the tests were conducted on teeth having a cycloidal profile instead of an involute profile.Cycloidal teeth were in general use in the nineteenth century because they were easier to cast than involute teeth.Equation(14-4a) is called the Barth equation.The Barth equation is often modified into Eq.(14-4b),for cut or milled teeth.Later AGMA added 50+√F K= (hobbed or shaped profile) (14-5a 50 Ku= 78+√7 (shaved or ground profile) (14-56) 78 In SI units,Eqs.(14-4a)through (14-5b)become Ky= 3.05+V (cast iron,cast profile) (14-6al 3.05 6.1+V K= (cut or milled profile) (14-66) 6.1 Ky= 3.56+F (hobbed or shaped profile) (14-6c 3.56 K= 5.56+√厅 (shaved or ground profile) (14-6d 5.56 where Vis in meters per second (m/s). Introducing the velocity factor into Eg.(14-2)gives 0= KW'P FY (14-7刀 The metric version of this equation is KWr 0= (14-8) FmY where the face width F and the module m are both in millimeters (mm).Expressing the tangential component of load W in newtons (N)then results in stress units of megapascals (MPa). As a general rule,spur gears should have a face width F from 3 to 5 times the circular pitch p. Equations(14-7)and(14-8)are important because they form the basis for the AGMA approach to the bending strength of gear teeth.They are in general use forBudynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 14. Spur and Helical Gears © The McGraw−Hill 717 Companies, 2008 Spur and Helical Gears 719 In the nineteenth century, Carl G. Barth first expressed the velocity factor, and in terms of the current AGMA standards, they are represented as Kv = 600 + V 600 (cast iron, cast profile) (14–4a) Kv = 1200 + V 1200 (cut or milled profile) (14–4b) where V is the pitch-line velocity in feet per minute. It is also quite probable, because of the date that the tests were made, that the tests were conducted on teeth having a cycloidal profile instead of an involute profile. Cycloidal teeth were in general use in the nineteenth century because they were easier to cast than involute teeth. Equation (14–4a) is called the Barth equation. The Barth equation is often modified into Eq. (14–4b), for cut or milled teeth. Later AGMA added Kv = 50 + √V 50 (hobbed or shaped profile) (14–5a) Kv =  78 + √V 78 (shaved or ground profile) (14–5b) In SI units, Eqs. (14–4a) through (14–5b) become Kv = 3.05 + V 3.05 (cast iron, cast profile) (14–6a) Kv = 6.1 + V 6.1 (cut or milled profile) (14–6b) Kv = 3.56 + √V 3.56 (hobbed or shaped profile) (14–6c) Kv =  5.56 + √V 5.56 (shaved or ground profile) (14–6d) where V is in meters per second (m/s). Introducing the velocity factor into Eq. (14–2) gives σ = KvWt P FY (14–7) The metric version of this equation is σ = KvWt FmY (14–8) where the face width F and the module m are both in millimeters (mm). Expressing the tangential component of load Wt in newtons (N) then results in stress units of megapascals (MPa). As a general rule, spur gears should have a face width F from 3 to 5 times the circular pitch p. Equations (14–7) and (14–8) are important because they form the basis for the AGMA approach to the bending strength of gear teeth. They are in general use for