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1 selection of involute gear displacement coefficient The key problem of displacement gear design is to correctly select the displacement coefficient. If the displacement coefficient is properly selected, the bearing capacity of the gear can be greatly improved. If the displacement coefficient is improperly selected, it will decrease. The carrying capacity of the gear. Regarding the selection method of the displacement coefficient, in recent years, the selection of the displacement coefficient by the "closed diagram" method has been generally paid attention to and popularized. According to the transmission requirements of the gear, various performance indicators can be comprehensively considered to determine the change reasonably. Bit coefficient.
However, due to its inconvenient use, people have established a cylindrical displacement gear design platform that satisfies the basic principle of selecting the displacement coefficient, and selects the displacement coefficient of the cylindrical gear, geometric calculation, and transmission quality inspection.
11 Knowing the center distance According to the principle of equal sliding coefficient, the displacement coefficient is selected as a pair of displacement gear transmission. To achieve no backlash engagement, the following formula must be satisfied:
η'=η′′η′=(1 z1z2)tanα′t−tanαB2tanαB2η′′=(1 z2z1)tanα′t−tanαB1tanαB1(1) where αB1 and αB2 are the lowest points of the gear section of gear 1 and gear 2, respectively Pressure angle.
tanαB1=tanα't-z1z2(tanαa1-tanα't)tanαB2=tanα't-z2z1(tanαa2-tanα't)
(2) When the gear center moment a' is given, the meshing angle of the end face is α't=acos(acosαta'). (3) According to the no-gap meshing equation, the sum of the two-wheel displacement coefficient is obtained:
XtÏ=xt1 xt2=z1 z22tanα(invα't-invα)
(4) When the central moment a is given, the sum of the displacement coefficients of the two rounds xt∑ is a constant, then there is only one independent variable in xt1 and xt2. If xt1 is an independent variable, the sliding of the roots of the two gear teeth The coefficients η′ and η′′ are both functions of xt1, and the problem that the sliding coefficients of the roots of the two gear teeth are equal is to solve the equation f(xt1)=η′-η′′=0(5) with xt1 as a variable.
12 Calculate the geometry of the cylindrical gear (see 1)
1 Involute cylindrical gear geometry Table 23 Check the gear transmission quality index According to the literature, check the gear transmission quality indicators.
1) A pair of displacement gear transmissions, in order to achieve no backlash meshing, the geometry of equation (6) must be satisfied; invα't=2(xn1 xn2)z1 z2tanαn invαt(6)2) to ensure that the gear processing is not rooted Cut; xn≥h3an-zsin2αt2cosβ(7)3) to ensure the necessary degree of coincidence; 12π(z1(tanαa1-tanα't) z2(tanαa2-tanα't)) bsinβπ≥ε(8)
4) Ensure that the gear does not interfere when meshing; gear 1 has no transition curve interference condition tanαt-4(h3an-xn1)z1sin2αtcosβ≤tanα't-z2z1tanαa2-tanα't(9) Gear 2 has no transition curve interference condition tanαt-4(h3an -xn2)z2sin2αtcosβ≤tanα't-z1z2tanαa1-tanα't(10)5) Guaranteed a certain tooth thickness; da1zπ2 2xttanαt invαt-invαacosβ≥s3a(11)
2 cylindrical displacement gear design platform involute cylindrical gear program flow as shown in Figure 1, in the involute cylindrical gear design, the known center distance first calculate the meshing angle, select the displacement coefficient according to the principle of equal sliding coefficient, determine the displacement The sum of the coefficients determines the variation coefficient of the center distance, assigns the displacement coefficient according to the string root method, calculates the geometrical dimensions of the two wheels, and calculates the gear transmission quality according to Equations 6 to 11, and the results are obtained.
The visual design platform of the involute cylindrical displacement gear developed by VB is as shown in the figure. When the known gear teeth are 16 and 50 respectively and the center distance is 274 mm, the design platform is used to design the displacement cylindrical spur gear. Firstly, the calculation of the displacement coefficient is calculated in the box, x1=0161, x2=017991; then the involute cylindrical gear size calculation is carried out, and finally the transmission quality check can be performed, and the gear 2 has the tip tip sharpening phenomenon, and the output result is obtained. .
3 Conclusion In the design of involute cylindrical gear, develop the visual design platform of involute cylindrical displacement gear. It is known that the center distance first selects the displacement coefficient according to the principle of equal sliding coefficient, then the involute cylindrical gear size calculation, and finally Transmission quality check, the software can easily determine the value of the engagement angle under the constraints.