American Journal of Technology and Applied Sciences 
ISSN (E): 2832-1766        Volume 31, December - 2024                              

 

P a g e  | 13  www.americanjournal.org 

 

ABOUT LIMITS OF THE FORCE SHOULDER FROM THE 

GENERATOR TO ROLLING ELEMENT OF BEARING 
Urinov N. F. 

Saidova M. Kh.  

Associate Professors of the Department of TM and MT 

 

Aminov M. Kh.  

 Master of Group M7-23 MICHADK 

Bukhara Engineering and Technological Institute 

 

A B S T R A C T K E Y W O R D S 

The article presents calculations for determining the force arm 

from the generator to the rolling element in order to determine 

the value of the generator force from the magnitude of the arm 

on the desired rolling elements 

Pressure angle, wheel profile, 

generator pressure angle, 

rolling body, force arm, gear 

ratio, radius of rolling bodies, 

reaction, generator, wheel. 

 

 

Introduction  

Rolling elements are an integral part of modern technologies. These mechanisms must have high 

productivity, operate under high loads and high wear. To calculate these loads and design highly 

efficient mechanisms, it is necessary to know the reactive forces, stresses, force arms and pressure 

angles of these elements. 

In addition to the force from the generator, the rolling element in the mechanism under consideration 

is affected by reactions from the separator and the profile wheel. In Figure 1, the transmission section 

with the rolling element and sections of the conjugate elements is taken separately to construct the 

calculation scheme of the forces. 

 
Figure 1 - Reactions of the rolling element from the side of the generator, separator, and profile wheel. 



American Journal of Technology and Applied Sciences 
31, December- 2024 

 

 
P a g e  | 14  www.americanjournal.org 

 

2 

1 2 

Pg   -rreaction from the generator,k– reaction from the profile wheel,𝑃s -рreaction from the 

separator,𝜓-atgenerator pressure point on the rolling element,𝛾– angle of pressure of the profile wheel 

on the rolling element 

 

To determine the numerical values of angles𝜓And𝛾Olet's fraternize withrwork [1]. 

Thus, to determine the angle𝜓Olet's turn to formula (1): 

                                          (1)ψ = arcsin((
𝑒

𝑟2
) sin(β)) 

Where 𝑟– radius of the centers of the rolling elements. 

To determine𝛾we enter the values of radial and tangent 

components of speed𝑉 and 𝑉. 

   𝑉1=−𝑒𝑡𝑔(𝜓)cos(𝛽) − 𝑒𝑠𝑖𝑛(𝛽) (2) 

                                             𝑉2 = (3)
𝑆

𝑖𝑜
 

Where𝑖0– gear ratio; 

𝑆- the distance from the center of the generator to the circle of the centers of the rolling elements; 

𝑒– transmission eccentricity; 

𝜓- atgenerator pressure point on the rolling element; 

𝛽– angle of rotation of the input link. 

Ratio for(4): 

γ = |𝑎𝑟𝑐𝑡𝑔
𝑉1

𝑉2
| (4) 

ABOUTReferring to (Fig. 3) we compose a system of equations of static equilibrium (5,6): 

    𝑃g cos(𝜓) − Pk cos(𝛾) = 0 (5) 

      −𝑃s – 𝑃k sin(𝛾) + 𝑃g sin(𝜓) = 0 (6) 

  Pabout the relation (5) we express(7): 

                                                        𝑃k= (7)−
𝑃 𝑐𝑜𝑠(𝜓)

cos (𝑦)
 

Underputting (7) into (6) we express𝑃s(8): 

𝑃𝑠 = 𝑃𝑔 = (
− cos(𝜓) sin 𝛾+cos 𝛾 sin 𝜓

cos 𝛾
) (8) 

Next, to determine the shoulders, let's refer to Figure 2:𝑎𝑖
𝑟 

 

 
Figure 2 - Geometric diagram for determining the lever arm hg from the generator to the rolling element 



American Journal of Technology and Applied Sciences 
31, December- 2024 

 

 
P a g e  | 15  www.americanjournal.org 

 

2 

Let us consider triangle OO1A in Figure 4. Let us determine the height of this triangle hg, which 

corresponds to segment CO. To determine this height, let us use formula (9): 

𝐶𝑂 =
2

𝑂1𝐴
√𝑃(𝑃 − 𝑂𝑂1)(𝑃 − 𝑂𝐴)(9) 

where P is the semiperimeter of triangle OO1A. 

This formula is obtained by determining the height throughthe value of the semi-perimeter [2]. 

We determine the value of the semiperimeter using formula (10): 

                                                     𝑃 =
𝐴𝑂1 + 𝑂𝐴 + 𝑂𝑂1 (10)

 

Let's determine the values of the segments: 

𝐴𝑂1 = 𝑟𝑡 + 𝑟𝑡𝑘 (11) 

                                                      O (12𝐴 = 𝑆𝑡 + 𝑟𝑡𝑘) 

                                                      𝑂𝑂1 =𝑒(13) 

Where 𝑒– transmission eccentricity; 

𝑆-distance from the center of the generator to the circle of the centers of the rolling elements; 

𝑟2– radius of the circle of the centers of the rolling elements. 

Distance𝑆will be determined by the following formula: 

𝑆 = ecsc 𝛽 + √𝑟2 − 𝑒2 sin(𝛽)2(14) 

Thus, formula (9), taking into account the above values, 

we rewrite the segments as: 

𝑃 =
𝑟2+ S + 2𝑟𝑡𝑘 

+ e 

2
     

(15) 

Underputting (15) into (9) we obtain the following formula: 

𝐶𝑂 =
2

𝑟2+𝑟𝑡𝑘
√𝑃(𝑃 − 𝑒)(𝑃 − 𝑟2 − 𝑟𝑡𝑘)(𝑃 − 𝑆 − 𝑟𝑡𝑘  (16) 

The length of CO corresponds to the desired value of hg, respectively. 

                                                          

Conclusion 

Using Microsoft Excel software, it is possible to determine each value of the hg arm and, by 

substituting it into the formula for finding the force from the generator on any rolling element, 

determine the values of the generator forces from the value of the arm on the desired rolling elements. 

 

References 

1.ShiBinsky K.G., Efremenkov E.A., An I-Kan Calculation of geometry and kinematics analysis flat 

To OuchrAdial ptransmissions with prOintermediate rolling elements 

//Theory and practice of gear transmissions and gearbox engineering: Collection of reports onatinternal 

technical conference with international participation - Izhevsk, Izhevsk State Technical University. - 

3-5 Dec. 2008. - Izhevsk: Publishing house IzhSTU. - 2008. - pp. 193-196 (58410462) 

2.Minyuk S. A. Mathematics for engineers: textbook in 2 volumes // Minsk: Elaida. - 2006. - V. 2.