INTRODUCTION The micro-segment gear is a new type of meshing gear. The tooth profile curve is not a single curve, but a curve similar to a stepped arc profile formed by a number of micro-segments according to a certain rule. The principle of its formation is described in detail.
According to the previous research results, the bending capacity and contact bearing capacity of the micro-segment gears are much better than the corresponding involute gears. This paper will further study the bearing capacity of micro-segment gears from the perspective of gluing load capacity.
Gluing of the tooth surface is a common form of gear failure. Once gluing occurs, it will expand rapidly, causing tooth surface damage, resulting in reduced gear load capacity and even fracture.
1 Calculation method selection 1.1 Tooth surface glue calculation method At present, the internationally authoritative glue calculation methods are: ISO glue bearing capacity calculation; AGMA aerodynamic spur gear, helical gear gluing calculation guide and Pegasus company's elastohydrodynamic calculation instruction manual.
The AGMA method is similar to the ISO method in that it is based on temperature. The method of the Pegasus company is based on the thickness of the oil film. China's GB/T6143-1986 is based on ISO, and the integral temperature method proposed by WinterH is the guiding method. In recent years, many scholars have proposed to design and calculate the lubrication problem of gears according to Dowson-Higginson's minimum film thickness formula.
Gear gluing calculations are a complex gear tribology problem, and no single method can be applied to all situations. Each of the above calculation methods has its own scope of application and should be selected according to the specific circumstances.
1.2 Selection of the calculation method of micro-segment gear gluing The above-mentioned gluing calculation method can be divided into two major methods: the internal temperature method of temperature criterion, the integral temperature method and the minimum oil film thickness method of film thickness criterion. The last method It is to control the film thickness ratio, and its mechanism is elastic fluid dynamic lubrication.
Compared with the involute gear, the micro-segment gear can withstand greater loads when it is meshed and transmitted. Therefore, the factor that the viscosity of the lubricating oil changes with the change of pressure (viscosity effect) must be considered, and the teeth are elastically deformed under the action of pressure. According to the transmission characteristics of the micro-segment gear, it can be determined that the micro-segment gear is extremely advantageous for forming an oil film. Therefore, the lubrication problem of the micro-segment gear transmission belongs to the category of elastic fluid dynamic lubrication (EHL) and should be solved by the theory associated with it.
Therefore, this paper selects the oil film thickness criterion to calculate the micro-segment gear gluing.
1.3 Oil film thickness method This method applies the EHL theory to the design of gears. By calculating the ratio of the minimum oil film thickness of the gear meshing point to the sum of the surface roughness of the two teeth (ie, the film thickness ratio), the lubrication between the tooth surfaces is estimated. State, and determine the gluing load capacity of the tooth surface.
1.3.1 Minimum oil film thickness formula According to the research conclusions of Dowson and Toyoda, the formula of the minimum oil film thickness hmin of the heavy-load contact zone is hmin=3.06G0.56U0.69W0.1n (1) where n is the gear pair method. To the comprehensive radius of curvature G, U, W - dimensionless parameter material parameter G = Er (2) - pressure - viscosity coefficient Er - comprehensive elastic modulus velocity parameter U = 0ve2Ern (3) where 0 - Absolute viscosity of lubricant ve - entrainment speed load parameter W = xwnErn (4) where x - load distribution coefficient wn - unit normal load 1.3.2 film thickness ratio calculated film thickness ratio = hmin21 2 ( 5) In the formula, 1, 2 - the root mean square value of the surface roughness of the large and small gears and the arithmetic mean value Ra of the surface profile have the following relationship = 1.25Ra1.3.3 Glue determination When the gear is 3, the tooth contact surface is formed. The stable oil film is a full-film elastohydrodynamic lubrication state, which avoids the occurrence of scratches and gluing.
When <1, no elastohydrodynamic lubrication is formed between the tooth contact surfaces, which belongs to the boundary lubrication state, and it is easy to cause damage such as gluing.
When 3>>1, it belongs to the partial elastohydrodynamic lubrication state, and the tooth surface is in the probability of being glued. In this case, it is not possible to judge whether or not gluing will occur based on the value alone, and it is judged based on other conditions such as the running condition.
In short, at a small time, due to the peak-top interaction of the rough surface, there may be both elastic deformation and plastic deformation, and the occurrence of gluing is related to such plastic deformation. Therefore, the condition in which gluing does not occur is usually defined as >3.
2 Problems that should be paid attention to when calculating. Due to the limitation of space, this article will not introduce them in a similar way to involute gears. Here, the uniqueness of the calculation of the micro-segment gear gluing caused by the different tooth shapes is briefly introduced.
2.1 Calculation of the comprehensive curvature radius It is known from the formation principle of the micro-line segment tooth profile that the tooth profile of the micro-line segment is composed of a large number of zero points, and the composite curvature at the zero point is zero (that is, the comprehensive curvature radius is infinite). Therefore, only non-zero points will be considered. The problem of calculating the comprehensive radius of curvature at the location.
2.1.1 Curvature radius of the end face The radius of curvature of the face tooth surface is shown in Fig. 1. It can be seen from the forming principle of the micro-segment tooth profile that the non-zero tooth profile is actually an involute of a continuously changing position, if the middle position of the involute of the micro-segment between the i-th and i-zero zero points is indicated by the following i (this At the same time, the oil film is the thinnest. At the same time, note that the micro-segment gear is convex-to-concave. The radius of curvature of the end-face profile is 1i=asinitu-1(6)2i=asinitu-1u(7)(6) In the formula (7), u denotes a gear ratio; it denotes an end face pressure angle at the i-th zero point.
Note that the micro-segment gear is convex-to-concave meshing, and the relative curvature radius of the end face is ri=1i2i1i-2i(8)2.1.2 The calculation of the normal relative radius of curvature is set. The helix angle of the helical gear is the normal relative curvature. The radius is ni=ricos(9). Note that since the difference is very small, the helix angle is used instead of the i-th segment base circle helix angle bi.
2.2 Entrainment speed According to the theoretical model of hydrodynamic lubrication, the entrainment speed of the two sliding surfaces is half of the tangential velocity of the two moving surfaces. Therefore, the calculation of the entrainment speed is actually the calculation of the tangential velocity.
Let the pinion radius be r1 and the rotation speed be 1. For the i-th micro-segment involute, because the arc length is extremely short, the micro-segment involute length S can be used instead of the tangential length, according to the literature [1] ,7,8], there is S=rbiu2u2u1(10)u1=r1sini-yisinirbiu2=r1sini 1-yi 1sini 1rbi 1(11) where i=arctan(xi-xi 1)(yi-yi 1)(12)xi , yi, xi 1, yi 1 respectively represent the coordinates of the i-th and i-th zero points, and the calculation formula is referred to the above related documents.
Figure 2 tangential velocity calculation reference map If the time to turn the micro-segment is t, then there is t=i 1-i1(13), so the tangential velocity is v-cut 1=St(14). The tangential speed of the gear, and the arithmetic mean of the two is calculated to obtain the entrainment speed.
3 Application example A pair of micro-segment gears used in a reducer, the modulus is mn=3mm; the number of teeth of the large and small gears is z1=17, z2=56; the helix angle is=11.75°; the arithmetic mean of the surface roughness of the gear is Ra1= Ra2=3.2; lubricating oil kinematic viscosity is 90cst; micro-segment 4 concluding remarks (1) through finite element calculation analysis and experimental verification, after the thin-walled cylindrical parts are subjected to the radial concentrated load, the loading point cross-section will produce complex lateral and longitudinal deformation. . Attention should be paid to the preparation of such parts for processes subject to radial concentrated loads.
(2) Using Shell143 shell unit, using ANSYS software for finite element analysis and calculation, the deformation value of thin-walled cylindrical parts subjected to radial concentrated load can be obtained. Generally speaking, the experimental results and the calculation results have little error, which indicates that the numerical method can be used to analyze the processing problems of thin-walled cylindrical parts subjected to radial concentrated load processing.
(3) In the straightening process of thin-walled pipe parts, the finite element simulation is used to calculate the overall deformation caused by the pressurization of the intermediate points of such parts, and the relationship between the straightening residual deformation and the reduction amount at the loading section of the part can be established. According to the principle of the reverse curve alignment, the table determines the required reduction.
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