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The gear mechanism can transmit the movement and power between any axis of the space. It has the characteristics of smooth transmission, wide application range and long service life. It is widely used in mechanical transmission. This paper studies the spur gears commonly used in railway locomotive transmission. In the theoretical design process, according to the basic law of gear tooth profile engagement, the common tooth profile curves of known tooth profiles and their meshing lines can be derived analytically, and the changes of important physical parameters such as gear ratio and coincidence degree are further studied. law. In practical applications, when the tooth profile deviates from the theoretical design value due to wear deformation, the meshing performance between the gears deteriorates, and the moving speed of the meshing point changes. At this time, the analytical expression of the tooth profile and the meshing line of the gear cannot be determined. In order to study in detail the gear transmission process in actual work, the basic conditions of tooth profile engagement are given in this paper. Based on this, a numerical model of the gear transmission was established.
1 The tooth profile engagement condition of the worn spur gear is a schematic diagram of the gear transmission consisting of two interacting tooth profiles. The figure shows the coordinate position of the meshing points of the two gears. Aiyi and x202y2 are the motion coordinate system rotating with the two gears and the Z302F3 are respectively fixed coordinate systems fixed on the two gear shafts. The parametric equations of the two conjugate tooth profiles are respectively set to 1 especially 2: the basic conditions of the two interacting gear teeth are the axial distance; (especially (P)) and (hair (P), K (P) ) is the coordinate of the meshing point P in the double and the coordinate system; the heart and M are the intersection angles of the common normal line and the coordinate axis of the meshing point. And inside. As shown. The two basic assumptions about the physical characteristics of the gear meshing are implied in the conditional equations (2): the two gears are rigidly fixed on the shaft, and the axial distance remains the same; the two tooth faces are tangent at any time during the transmission. The equation for determining the P coordinate of the meshing point is the numerical model of the tooth profile and the meshing line of the formula (3) 2. Using a large amount of data obtained by measuring the gears in the electric locomotive gearbox, the tooth profile is established by various methods by means of a computer. A numerical model of the meshing line. Based on this, the variation law of the physical parameters such as the gear ratio and the coincidence degree of the gear is studied, and the real process of the gear meshing motion is further simulated. The following is the process of establishing a numerical model of meshing motion using the mathematical software MathCAD.
By sampling and measuring the coordinates of the position of each point on the gear surface, the analog equation of the tooth profile is established by MathCAD: y> =fiW, (i=l, 2 respectively represent the two common tooth profiles), and the simulation diagram of the tooth profile is drawn. The shape is as shown.
To solve the equation (3), a numerical expression of the first derivative of the tooth surface must also be found. In the case of small steps, the numerical simulation function of the tooth profile h=(4 in the motion coordinate system and the derivative on the motion coordinate system, which can be expressed as fpr; U) in the shape of the tooth profile is shown by means of the approximate approximation.
After obtaining the profile simulation curve of the driving wheel and the passive wheel, the driving wheel angle is arbitrarily designated. =pw(t), according to equation (5), the final character of the set of dynamic equations can be obtained. And the coordinates of the meshing point P in the motion coordinate system. In solving by numerical method, in order to minimize the difference between the left and right ends of the equations, the Minner function of MathCAD is used in the motion coordinate system force and 22y2, and the third-order Spline approximation method of transition point interpolation is adopted.
The trajectory of the meshing point P in the equation (5) is the meshing line.
The example of the tooth profile simulation curve profile derivative curve 3 is taken as an example of a spur cylindrical involute traction drive gear in a gearbox of an electric locomotive. The design parameters are pressure angle = 21°34", and the theoretical meshing length is 45.64mm. As shown, both the driving wheel and the passive wheel are new gears. The meshing line obtained from the model based on the measured data is AW, the theoretical meshing line. ATAT'. The pressure angle calculated from the mold type = 21 ° 20", the length of the meshing line A7V = 45.62 mm. The meshing process of the wear gear in some cases is given in the meshing line and the pressure angle. Where: (a) the meshing line AB of the two tooth profiles when the driven wheel is slightly worn and the driving wheel is a new gear; (b) the meshing line of the two tooth profiles when the driven wheel is severely worn and the driving wheel is a new gear; (c) the driving wheel The line of twisting of the two tooth profiles when the passive wheel is a new gear; (d) the meshing line of the two tooth profiles when the driving wheel and the passive wheel are severely worn.
Medium (a), (b) respectively give the wearer's passive wheel corresponding to the tooth profile in both (a) and (b). (b) The passive wheel is severely worn. The upper curve in the figure represents the ideal tooth profile, and the lower curve represents the tooth profile after wear.
When both conjugate tooth profiles are not subject to wear, for example, the meshing line is straight, and the gear ratio during the meshing process remains unchanged. When there is slight wear such as (a), the meshing line is slightly deformed. When the wear is severe, such as (b), the meshing line is greatly distorted.
The length of the actual meshing line is also different due to the different degrees of tooth surface wear. In order to ensure the continuity and stability of the transmission, to determine whether the worn gear can continue to be used, the conditions should be met: coincidence s > instantaneous transmission ratio i during the meshing process (= still. (/. (, can be given by MathCAD) When the tooth surface wears, the gear ratio is deformed, so that the gear ratio during the meshing process is no longer constant, and the wear degree increases more severely, which also destroys the smooth characteristics of the gear transmission.
The meshing line of the A yoke profile with different degrees of wear is different. The tooth profile of the passive wheel is 4. By measuring the gears in the gearbox of the railway locomotive, the mathematical model of the gear meshing process is established by computer to simulate the transmission process. the study. After a long period of high-load operation, the gears in the gearbox will wear and deform to varying degrees. Using the above method, the gear transmission characteristics can be analyzed in detail, the stability and reliability of the gear transmission process can be monitored and the gear life can be measured more effectively. In the gear transmission process, due to the different degrees of tooth surface wear of the driving wheel and the driven wheel, this numerical simulation method can be used to re-match the worn old gears, thereby extending gear life, improving transmission characteristics, and saving gear manufacturing. cost.
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