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The other family equation is the date of receipt 2, 0614. Author brief introduction Wu Lianyin 1974. Male. PhD student; Wang Xiaoyu contact, male, professor, doctoral tutor.
From a mathematical point of view, Equation 2 separates the two-degree-of-freedom envelope of 6 and . Therefore, when the extension of the epicycloidal hypoid gear is processed by the development method, if the enveloping process of 0 and is still separated, the analysis can be performed by the same method. Actually. You can still meet the purpose of imagining the plane production wheel.
1 When the tooth surface equation of the imaginary flat-shaped wheel is processed by the forming method, the tooth surface of the workpiece is the edge of the blade, and the sub-envelope can also be studied. In general, the sub-envelope method is more convenient to understand and solve. The basic idea is to first fix a parameter to make another parameter 2 change to form a sub-envelope and a linear enveloping for its debounce or track surface.
The parameter 1 of the sub-envelope surface containing the parametric test 1 was changed. To form a sub-envelope surface. Normally, the next envelope surface will change not only in the position of the space with the change test 1. Its shape also varies with it. For some specific situations. If a special equivalent treatment is used. So that the shape of the sub-envelope surface does not change with the parameter variable 1. It is also a function of parameter variable 1. Thus, the enveloping process degenerates into the motion envelope of the sub-envelope with a constant shape. Make the analysis process simple for everyone.
According to the analysis, the mountain can be changed at the determined development time to form the trajectory surface of the blade on the workpiece, and the tooth surface of the workpiece is the enveloping surface of the curved surface of the blade. From the equation of the blade trajectory surface in Document 1, it can be seen that not only the position of the blade trajectory surface changes, but also its shape changes. Therefore, it is very difficult to directly solve the tooth surface equation and perform differential analysis by the envelope method.
Studying the surface equation of the blade trajectory, it can be found that the shape changes with the change of the position of the cutter axis and the workpiece axis. Therefore, if it is assumed that there is an imaginary gear, the relative position of the axis and the axis of the cutter head does not change during the development process, and if the relative movement of the imaginary production wheel is equivalent to the division of the cutter head and the workpiece Movement, which defines the imaginary gear; the face is defined as the shape of the blade about its axis, and the edge of the envelope can be separated from the envelope. Habit 1 refers to this imaginary gear as a hypothetical production wheel, whose tooth surface is called a shape. The factory is through such an equivalent transformation. It is possible to convert the two-parameter entanglement process of the blade into a motion envelope of the shape + the second sub-network. The motion envelope relationship is the relationship between the heart shape and the workpiece.
The concept of the imaginary production wheel in the type of machine tool is different from the concept of the imaginary production wheel in the traditional cradle machine. In the traditional cradle-type machine tool, the axis of the imaginary production wheel coincides with the axis of the cradle, and the position is unchanged during the development of the machine. The axis of the imaginary production wheel and the cutter head are moved. The axis is fixed, so the axis of the imaginary production wheel moves with the cutter.
In the initial position, how the axis position and the number of teeth of the imaginary production wheel are determined, and how it relates to the tooth surface of the workpiece. Therefore, the following theorem needs to be proved first.
1.1 The imaginary shape wheel theorem Theorem At the arbitrary development time, when the 0 changes, the trajectory surface formed by the blade on the workpiece is the same as the trajectory surface of the imaginary gear tooth profile on the workpiece, and the position of the imaginary production wheel The number of teeth is irrelevant.
It is proved that the tooth surface of the hypothetical production wheel already exists. After the cutter head rotates through the angle 0, the imaginary production wheel must rotate the angle of the blade around its axis to fit the tooth profile of the production wheel. In the initial position, the bait surface equation is r point and radius vector B, which is the indexing movement speed ratio between the blade and the imaginary production wheel; B is the number of the cutter head; the number of imaginary gear teeth; The symbol factor is determined by the rotation of the cutter head and the axis of the production wheel.
The production wheel and workpiece obtained at this time are stationary + moving in the machine coordinate system. To form the trajectory surface of the blade on the workpiece, the relative movement of the cutter head and the imaginary production wheel is equivalent to the indexing movement of the workpiece of the cutter head 4. Then the corresponding knives turn over the angle 0, the imaginary production wheel must be rotated correspondingly to the angle of 0. The piece should be turned over the angle, 9. This, the tooth profile of the production wheel coincides with the trajectory surface of the blade on the workpiece. , that is, in the forming position, in the initial position. The surface equation of the blade path on the workpiece is the tooth surface shape of the imaginary gear in the trajectory surface of the 3rd generation type 4, f; Ra, ni6a2 is the same as the formula 1, which proves that the blade forms a closed on the workpiece. In fact, in the wheel train of the imaginary production wheel and the workpiece, the imaginary production wheel is an idler wheel, and the above conclusion just proves this.
On the 1.66 type machine, the imaginary wide wheel axis is taken as a constant surface-shaped wheel formed by the flat axis of the cutter head and fixedly connected.
The intersection line between the tooth line plane and the tooth surface of the imaginary plane-shaped wheel is an extended epicycloid. After the position of the production wheel is determined. In order to ensure the correct meshing relationship, the positive number will also be reversed. 1.2 The tooth surface equation of the imaginary plane-shaped wheel is on the 0-type gear machine. In the initial position, the axis of the imaginary plane-shaped wheel coincides with the 2-axis and is fixed to the axis of the cutter head. The axis moves around the axis of the workpiece through the center of the machine. Yes, the cutter head axis is. Driven by 1 axis, the axis of the imaginary plane production wheel in the machine tool is flat with the cutter head. The equation of the profile surface is that the trajectory surface equation of the blade on the workpiece is rs.Ra, and the a2 and the formula 2 have In the same form, the tooth surface of the workpiece is the 乜 surface formed by the forming motion relationship between the workpieces.
1.3 The number of teeth of the imaginary plane-shaped wheel According to the hypothetical shape-shaped wheel theorem, in the initial position, the pitch circle center of the imaginary plane-shaped wheel can be set to coincide with the apex of the workpiece gear cone, so the pitch circle radius is equal to the midpoint cone of the workpiece gear. Distance, that is, the pitch of the midpoint of the gear section cone; 8 is the taper angle of the workpiece gear section. So it is a flat crown wheel, which is the same as the imaginary plane shape wheel; when the 3-sided production wheel is delayed into a rack, this is the result of the usual conclusion.
2 The mathematical significance of the imaginary plane-shaped wheel is mathematically significant. The imaginary plane-shaped wheel is actually the constant shape of the formula 1. The definition of 3 vector rotation shows that the operator R is known by the forming principle analysis. The operator R is then transformed into the formula 1, so that the above formula can be turned into the same as the formula 18 and the above formula also proves the correctness of the conclusion from the mathematical meaning.
3 What is the difference between the parameters of the shape and the surface, so that the partial guides of the 5 and 0 can be obtained on the production plane, so that the partial guides of the production plane are obtained, and then according to the literature 4 The number, that is, the main anvil, the main rate is ... obviously they are. , and the function.
4 Tooth surface parameterization and differential structure analysis During the development of the motion, the production surface is driven by the cutter head and is translated in the machine coordinate system. The speed i=zi+2z2Hu+4z4f the workpiece rotates around the axis, and the shaft is in the light. In the plane, the axis of the 5-axis machine tool coordinate system rotates, and the angular velocity is spread at a point. Then, the speed of the piece is at the point of development, and the relative velocity of the forming surface and the workpiece is determined by the engagement equation. Yes, fVwfl gives the center 9. The order-to-differential geometric parameters of the production plane are determined and determined. From the analysis of the motion analysis method of Document 2, it is possible to obtain all the differential geometry parameters at the point on the tooth surface.
Il Wu posted Wei Hongqin. 1 hour. The tooth surface of the Yanzhong outer cycloidal bevel gear is opened and the new method of analysis is proposed. Called Journal of An Jiaotong University, 2003514346.
2 Zhang Yanhong, Wu Lianyin, Wang Xiaoyu, et al. Analysis of the geometric parameters of the type 1 surface. Mechanical Transmission, 1999, 2341315.
3 Wu Daren, Luo Jiayu. Gear meshing theory. Experimental Research on Forced Flow Boiling Heat Transfer of Liquid Nitrogen in Slit Channels by Beijing Science Press, edited by Sun Daliang, Wu Yuyuan, School of Energy and Power Engineering, Xi'an Jiaotong University, 71004, from Xi'an Forced flow boiling heat transfer in the channel. The experimental results show that the forced flow boiling heat transfer coefficient of the liquid nitrogen in the zigzag-shaped chisel channel is 3,5 times that of the traditional large straight-tube buffer boiling compared with the boiling heat transfer in the thermosiphon slit channel. When the trade degree is still at 101.7, the forced flow boiling has obvious advantages in heat transfer temperature difference and heat transfer coefficient. The liquid nitrogen forced flow boiling heat transfer coefficient increases with the increase of mass flow rate, and the trend of increasing heat flow density is more significant. The slit gap size is reduced, and the heat exchange effect is enhanced. The zigzag channel and the ring channel have a heat transfer effect in the same chord-shaped channel.
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