KINEMATICS AND MAIN DIMENSIONS OF SPUR GEAR CYLINDRICAL GEARS

Аннотация

This article presents theoretical information on the kinematics of spur gear cylindrical gears, theirmain dimensions, and the forces acting onthem, which are commonly used inthefield ofmechanics. Keywords: gear wheel, gear, parameters, diameter, forces, kinematics, speed, tooth module, numberof teeth, outer, inner circle. Introduction. Nowadays, in the field of mechanical engineering, in particular in the mechanization of agriculture, the use of gear mechanisms in many agricultural machines is of great importance. The importance of gear mechanisms in this is that they convert the rotational motion coming from the tractor's power take-off shaft into the working part of the machine [1-2]. When adapting the rotational motion to the movement of the working part, it is necessary that the materials and dimensions of the parts of this mechanism can withstand the stresses generated in the environment during movement and ensure smooth movement. For this reason, it is necessary to studythemovement ofgear transmissions,their parameters and theforces acting onthem [3-6]. Research method. Permanently attached couplings can be fixed or movable. Fixed couplings connect the shafts so that they do not slide relative to each other. Movable couplings connect the shafts inaway that allows them tomoveindifferent directions [7-10]. Research results and discussions. A gear wheel with a cylindrical gear and a pitch cylinder of thesidesurfaces oftheteeth parallel to thesides ofthe wheel iscalled aspurgear [11-13]. Cylindrical gears (Figure 1)belong to direct contact gears. Figure1.Cylindricalspurgear These gears are used at speeds ≤ 2 / . We determine the geometric parameters [ 14-15] of spur gear cylindrical gears depending on the moduleand number ofteeth (t and z). 151 INTERNATIONAL MULTIDISCIPLINARY JOURNAL FOR RESEARCH & DEVELOPMENT SJIF2019:5.2222020:5.5522021:5.6372022:5.4792023:6.5632024:7,805 eISSN:2394-6334 https://www.ijmrd.in/index.php/imjrd Volume12,issue06(2025) Fig. 2.Maingeometric parameters ofgear drives with tooth profiles Tooth tipdiameter (1) Tooth socket diameter = +2ℎ (2) From theequation = ,thediameter ofthedivisionis: = −2ℎ yoki (3) According to the standard, the height of the tooth head is h = m; the height of the tooth root is ℎ = ( ) = =1.25 ; Theheight ofthe toothis h=h +h =m +1.25m =2.25m. a f From here thediameterof thetooth tip (4) Tooth socket diameter = +2 = ( +2) (5) The difference between the height of the tip of one wheel and the height of the tread of the other = −2.5 = ( −2.5) creates radial clearance. (6) Thedistance between theaxes = w c = ℎ −ℎ = 1.25 − = 0.25 (7) 1+ 2 ( 1+ 2) In a gear, thewidth ofthetoothis equal to thepitch length: = = 2 = 2 m −tooth length coefficient (toothwidth)modulus The forces arising from the meshing of the teeth are applied to the teeth of the wheels, and then these are transmitted to the joints inwhich the wheels are mounted, from the shafts to the bearings and other parts [16-19]. To calculate the details listed above, it is necessary to know the magnitudeanddirection oftheseforces [20-23]. As shown in the figure, a pair of teeth participate in the connection, and we assume that the connection point coincides with the line N. The load in the tension distributed along the length of the line NN is replaced by the resultant force, which is directed along the connection line NN and is normal to the contours of the teeth at the connection point. Frictional forces in the connection are not taken into account, sincethey are small[24-28]. 152 INTERNATIONAL MULTIDISCIPLINARY JOURNAL FOR RESEARCH & DEVELOPMENT SJIF2019:5.2222020:5.5522021:5.6372022:5.4792023:6.5632024:7,805 eISSN:2394-6334 https://www.ijmrd.in/index.php/imjrd Volume12,issue06(2025) For practical purposes, not only the force is of interest, but also its components - the circumferential force F, tangent to the dividing circles, and the radial force F , directed along the t r lineconnecting the centers ofthewheels. Figure3.Determining theforces acting onthemeshing of gears F is thetotal force perpendicular to thetoothsurface alongthemeshing line. n From this, (8) (9) Here T ,T are thetorques onthegear and wheel, respectively; 1 2 d ,d -diameters of thegear and wheel pitch ofthe circle, respectively; 1 2 u–numberof transmissions. The direction of force on the driven wheel is in the direction of rotation, and on the leading wheel itis opposite[29-30]. Conclusion. According to the analysis of the theoretical data considered above, the forces acting on the gear mechanisms have a significant impact on the smooth movement of the mechanism, its kinematics. At the same time, the provision of the required torque due to the rotational force acting on the mechanism depends on the main dimensions of the gears, that is, it varies depending onthediameter oftheirpitch circle.