UA10470U - Toothed gear with modified in profile teeth - Google Patents

Abstract

A toothed gear comprises driving and driven toothed wheels with evolvent teeth placed on the those and being in coupling with each other. At the sections placed from the ends of the teeth of the driven toothed wheel at distance , the teeth are arranged skewed at angle with respect to the generatrix of the side surfaces of those, due to that the thickness of the teeth in end cross-sections is decreased by value . Parameters of the profile modification of teeth , , are determined by formulae.

Description

Description of the invention

The utility model refers to the field of mechanical engineering. 2 The gear transmission is known, which consists of the driving and driven gear wheels with involute teeth located on them, which through interaction with each other carry out the transfer of rotation and load from one shaft to other shafts of machines and mechanisms (1): Ossetsky N.S., Moiseenko E.N., Myasnikov G.V. etc. Applied Mechanics. M.: Mashinostroenie, 1977. - 488p.

The disadvantage of the known gear transmission is the limited load capacity in terms of contact stresses, which is determined by the influence of structural, technological and operational factors that lead to misalignment of the gear wheels relative to each other.

The closest in terms of technical essence to the proposed solution is the gear transmission with puncture correction of the teeth adopted as a prototype |2): Kudryavtsev V.N., Derzhavets Yu.A., Glukharev E.G.

Design and calculation of gears of reducers. - L.: Mashinostroenie, 1971. - 328p. 12 The disadvantage of the specified gear is the low efficiency during operation and the lack of calculation dependencies to detect the effect of tooth puncture adjustment on the load capacity of the gear when the gear wheels are skewed relative to each other.

The task of the useful model is to increase the load capacity of the gear transmission and establish the influence of the parameters of the profile modification of the teeth on the work efficiency of the transmission.

To solve the problem in the gear transmission, which consists of the leading and driven gear wheels with involute teeth located on them, which are in mesh with each other, according to a useful model, in the areas located from the ends of the teeth of the driven gear wheel at a distance of 5.4, the teeth are made beveled at an angle p relative to their lateral surfaces, in connection with which the thickness of the teeth in the end sections is reduced by the amount of 24 5, while the parameters of the profile modification of the teeth Bi, VD, A Z are found from the expressions: - sh- m Zu/2 r how are you

Te de r hriro(rozhri) - the specified radius of curvature of the teeth in the engagement pole; r 4-t8vipo d/2, r o-tlovipo mi? - radii of curvature of the teeth of the driving and driven gears in the engagement pole; 74, 72 - the number of teeth of the leading and driven gears; o U - engagement angle; the sign "-" for external, and the sign "-" for internal engagement of teeth; E 4 - normal force acting on a pair of teeth; E - modulus of elasticity - materials of gear wheels; lu - angle of misalignment of gear wheels relative to each other; o k - the coefficient that characterizes the ratio of the half-length B, - the contact area to its half-width Bo, which is found by 3o solution of the equation -- pli NI ots Mov! "

Comparative analysis with the prototype shows that the claimed gear transmission differs in that in the areas located from the ends of the teeth of the driven gear wheel at a distance of 5 4, the teeth are beveled at an angle p relative to their side surfaces, in due to which the thickness of the teeth in the end sections "z is reduced by 24 5, while the parameters of the profile modification of the teeth B, VD, A Z are based on the dependencies given below for the first time.

Fig. 1 shows a single-stage gear transmission of internal engagement; in Fig. 2 - in profile - 15 modified tooth of the driven gear wheel; in Fig. 3 and 4 - calculation models of contact of teeth in two mutually perpendicular planes 20ОХ and 20У; Fig. 5 - graphical determination of the coefficient o, k. (av) In accordance with Fig. 1-5 we have: su 4, F o - Angular velocities of the driving and driven gears; B. - the length of the section, within which the teeth are beveled; B, - length of teeth; p - bevel angle of the end sections of the teeth; A 5 - 5r The amount of tooth thickness reduction on one side in the end section; because, B; - half width and half length

Ш - contact areas; р 4, р » - radii of curvature of the side surfaces of involute teeth in the engagement pole; zu is the angle of misalignment of the gears relative to each other, and Oslu "x 0.001 rad. at; К-Бб/Бо - coefficient: ф (ok) - function of the coefficient о, к.

Gear transmission consists of leading 1 and driven 2 gear wheels with involute teeth З and 4 located on them. At the same time, teeth 4 of driven gear wheel 2 in sections 5 and 6, adjacent to the ends, have bevels 7 and 8, which are compared with the gear 9 corner D.. c Bevels of teeth 4 are made on sections 5 and 6 within the length of B. The middle part of 10 teeth 4 within the length of Bu, - 25, has no bevels. The side profiles of the teeth, the same applies to the side profiles of the teeth, are outlined by the involute curves 11 and 12. 60 When there is no load, the teeth Z and 4 in the 2Ox plane (Fig. 3) have contact at the point O, which coincides with the engagement pole. In the plane 20y (Fig. 4), where the tooth 4 is skewed in relation to the tooth Z by an angle y, the final one between the generating teeth 9 and 13, the specified teeth also contact at the point O, which coincides with the engagement pole.

Thus, when gear wheels are skewed relative to each other, there is a contact line that corresponds to an angle of 0, and a point. In this regard, in the presence of misalignment of the gear wheels, the gear engagement changes from flat to spatial engagement with turned contact.

Lines 14 and 15 (Fig. 4) characterize the axes of symmetry of the section of the profile-modified tooth 4 of the driven gear wheel 2.

To evaluate the efficiency of the proposed gear transmission, the solution of two spatial contact problems was performed. The first task determines the finding of the maximum contact stresses with it when the gears are skewed

The wheels are relative to each other, taking into account the profile modification of the teeth, namely: zi 50213 (equ o gi des k - a coefficient that takes into account the ratio of the half-length B of the contact area to its half-width Bo, which 70 is found from the expression of Ero Uriro roiri) - indicated radius of curvature of the teeth in the engagement pole; p 4-t248ipo;m/2, p 2-tl»ovipo; mi/2 - radii of curvature of the teeth of the driving and driven gears in the engagement pole; t - engagement module; 724 , 22 - the number of teeth of the driving and driven gears; о y - engagement angle; the sign "х-" for external and the sign "-" for internal engagement of teeth; Е , - normal force acting on a pair of coupled teeth; Е - module the elasticity of the materials of the gear wheels; lu - the angle of misalignment of the gear wheels relative to each other.

In order to find the maximum contact stresses c, in a traditional gear transmission with misalignment of gears, the teeth of which do not have a profile modification, a spatial contact problem is also solved, in connection with which we have sleep U pz, Oto Eta | 8) soets r de o; c is a coefficient characterizing the ratio of the length But of the contact area to its half-width Bo, which is found from the expression pava t speci MeV o

Let us denote the left parts of equalities (2) and (4), respectively, by fr (о; к) and ф (о; с). )-1 and f (o; c)-1.

To compare the effectiveness of the proposed and traditional gear transmission, we will perform calculations of single-stage gear transmission of external engagement with profile-modified and unmodified av! with straight teeth, based on the data: 7 1250; 72100; tebmm; -

B,-125mm; at 209; sf 0.15. 10 Betrayal; In 2 0.3. 10 Betrayal; Ep-4. 109H; E-2,1. 10 MPa.

Given the values o k-o, c-20; 60; 70; 80; 90 and 100, using formulas (2) and (4), we will find the values of the functions ф (о. ку) and Ф (о с) which correspond to the accepted values of ок ос: ф (о к)-1.694; 1,332; 1,084; 0.907; 0.776; 0.674"

Y f(oss) 2.121; 1,666; 1,359; 1,139; 0.974; 0.847.

Then in the coordinate system sf (o; k)-o. k and f (o; s)-o; c Based on the found values of the functions sf (о k) and Ф (ос), we will construct the following curves 16 and 17 (Fig. 5), based on which the found coefficients o; k-74 and o 0-84. z» According to formulas (1) and (3) at o K-74 and o 0-84 we find c, -849MPa and c,7-1033MPa. Thus, the contact stresses due to the profile modification of the teeth decreased by 1033/849-1.217 times, which is equivalent to increasing the load capacity of the proposed gear by 1.2173-1.8 times. -z 75 It should be noted that at D "2u the efficiency of the proposed gear transmission is lower than at Zu /2" r "du.

If we take the angle DV -Zu /2-0.225. 10Zrad, in this case the stress c nui-772MPa, in connection with which the stress sut decreases by 1033/772-1.338 times, and the load capacity of the proposed gear transmission, in comparison with the prototype, increases by 1, 3383-2.396 times.

From the above calculations, it is clear that due to the profile modification of the areas of the teeth adjacent to their ends, the load capacity of the proposed gear in terms of contact stresses increases by 2 to two or more times, which emphasizes its effectiveness in comparison with a gear that does not have a profile modification of the teeth .

Gearing works as follows.

When the engine transmits the torque and rotation frequency to the driving gear wheel 1, it assumes an angular velocity o 4. Tooth C of the driving gear wheel 1, acting on tooth 4 of the driven gear wheel 2, causes it to rotate with an angular speed o". At the same time, the involute teeth Z and 4, having side profiles in the plane 20ОХхx (Fig. 3) in the form of involute curves 11 and 12, roll against each other with sliding from the moment of their entry to the moment of exit from the engagement. because in the plane 20y (Fig. 4) the conjugated pair of teeth Z and 4, having contact at the point O, moves within the limits of the interaction of the involute curves 11 and 12 with each other at an angle m relative to the generating side surfaces 9 and 13.

When the coupled pair of teeth З and 4 is loaded by the force Е, in the 2Ох plane, the contact point О is transformed into the width of the contact pad 250, and in the 2О0y plane, the contact point О grows into the length of the contact pad 2B,. In accordance with what has been said, the engagement pole has a contact area of 4BoB. b5 At the moment of disengagement of the pair of teeth З and 4, the following pairs of teeth are alternately drawn into the engagement, which ensure continuity of rotation of the torque-loaded driving gear wheel.

The economic effect of the implementation of the proposed technical solution should be expected due to an increase in the load capacity and efficiency of the gearing.

The public benefit of the proposed technical solution consists in improving the vibroacoustic characteristics of the transmission due to the reduction of vibration and gamma (industrial sanitation), caused by more favorable conditions of contact interaction of profile-modified teeth of the driven gear wheel.

Claims (1)

The formula of the invention and Gear transmission, which consists of the leading and driven gear wheels with involute teeth located on them, which are in mesh with each other, which differs in that in the areas located from the ends of the teeth of the driven gear wheel at a distance in, , the teeth are beveled at an angle Р relative to their side surfaces, which is why the thickness of the teeth in the end sections is reduced by /5 Value 245, while the parameters of the profile modification of the teeth v, v, 45 are determined from the expressions: ОЕ ТИК с АВ- ДЬ, в - 1528И---- : ОО kaye 2 where d- dra di - the given radius of curvature of the teeth in the engagement pole; Dt NE vii a, /2, data v su u 2 - radii of curvature of the teeth of the driving and driven gears in the engagement pole; chr. 22 - the number of teeth of the leading and driven gears; y" - engagement angle; the sign "Ж" for the external, and the sign "-" Ж for the internal engagement of the teeth; and. - normal force acting on a pair of teeth; A - the modulus of elasticity of the alloy materials of gear wheels; "K - the angle of misalignment of the gears relative to each other; au is the coefficient characterizing the ratio of the half-length B of the contact area to its half-width B., which is found by solving the equation: o I cook vu " "c) є - and? - («c) sh» - and (42) 60 b5