Research on meshing impact of modified involute spur gear
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The meshing impact of the involute spur gear is an important factor affecting its performance. The calculation method of meshing impulse and meshing impact response of non-retrofit involute spur gears has been given. An effective measure to reduce the gear meshing impact is the profile modification. However, this does not completely eliminate the meshing impact, especially in the case of underload operation, there will be disengagement. The reasons for this problem are: 1) the principle error of the modified profile curve; 2) the gear has various manufacturing errors; 3) the change of the load condition. For a pair of meshing tooth pairs, the following meshing states may occur: 1) generating a biting impact and a biting impact; 2) the instantaneous coincidence of the biting becomes smaller but still greater than 1; 3) although generally In the case where the degree of coincidence is greater than 1, but the instantaneous coincidence of the biting is less than 1, causing a dislodge impact. This article will provide a quantitative description of the above issues, which can be provided for the correct use of the shaping gear and the search for new countermeasures.
1 Involute spur gear tooth profile modification 3 = r, / the biting section of the double tooth meshing zone, the non-shaping part of the active tooth profile meshes with the modified portion of the passive tooth profile. In the biting section of the double-tooth meshing zone, the condition is opposite to the biting section.
2 The intrusion (or meshing) impact of the involute trimming gear When the gear is overloaded or the machining accuracy of the gear is low, the impact and the impact are generated. The meshing impulses generated by these two kinds of impacts are approximately the same. The following is an example of the impact of the impact.
2.1 Passive tooth profile In the time interval Ar of the meshing line advancing in advance, gear 1 is the driving wheel, gear 2 is the driving wheel, and they are assumed to be standard gears, the center distance is a. The speed is cm, W2, and the number of teeth is Zi , Z2, the radius of the base circle is rbPrb2, and the radius of the tip circle is ra, ra2. Both gears are modified according to the method shown. When the tooth profiles 1, 2 are engaged with the unshaped portion in the single-tooth meshing region, at a certain time T, the tooth profiles 3, 4 come into contact at a point B other than the meshing line N-N. When the gear is operated for one week, the time is Tz=S. When the starting point of time is set at the theoretical moment of the tooth profile 3, 4, O1X2Y2 and O2X4Y4 in T are static coordinate systems, and O1X1Yi is rotated with the gear 1. In the moving coordinate system, O2X373 is the moving coordinate system that rotates with the gear 2. The unshaped part of the tooth profile 3 is in the moving coordinate system in the static coordinate system 01X2Y2, and the equation in the equation is O1X1Y1. The equation in the modified coordinate part of the tooth profile 4 is the stiffness of the tooth profile 1, 2 in the moving coordinate system O2X3Y3. K is a function of the position of the meshing point and can also be expressed as a function of time T. Under the action of the meshing force Pn, the compression deformation of the tooth profiles 1, 2 (specified as a positive value) Sl (T) = K, S2 (T) = K (y. They have a smaller angle, a large burning and , the trend of getting bigger.
The machining error of the gear can also affect the value of the angle 93. If the base deviation is ±/tooth tolerance is /f, then the probability is synthesized. The actual calculated value of the base difference is /=±1/2 (prescribed to make the base section positive when it becomes larger).
Since point B is a common point, there is a problem that B is obtained from equation (5) on the outer circumference of gear 2 by 12 points, = ± 2 - < 2. It is combined with equation (1), equation and equation (8). In a joint solution, the moment of engagement To can be obtained, and the time interval of early engagement is obtained. 2.2 The calculation of the engagement impulse Fi. The so-called meshing impulse refers to the engagement force Pn between the tooth profiles 3, 4! Integration over time interval AT.
When the tooth pairs 3, 4 start to contact but have not yet generated a biting force, the meshing force between the pair of teeth 1, 2 is P% but the actual load of the gear is Pn and therefore under AP = Pn - P%, the tooth pair 3 , 4 has a biting force Pn! .
It is a sketch of the state of engagement at T%. At point B of the cusp contact, the normal line M-M of the tooth profile 3 and the normal line Q-Q of the tooth profile 4 are not in a straight line. When solving the household, you can still use the above formulas (7), (8), (9), etc., except that T=Tx is used as the known quantity, and P=PMä¹ is the unknown quantity to solve. Find Px After that, 93, can be obtained.
In the direction of the mesh line N-N, the stiffness of the tooth profile 1 is Ki (TX), and the stiffness of the tooth profile 2 is K2 (TX). In the normal Q-Q direction, the stiffness of the tooth profile 4 is K2(T x+Tz) in the normal M-M direction, the stiffness of the tooth profile 4 is Kl (TA+TZ) and the stiffness of the tooth profile 3 is KT+M-Tz) ignores the effect of profile modification on the stiffness of the profile.
Let the meshing force between the tooth profiles 1, 2 add AP after the P x ​​is exceeded, and the tooth profile 1, 2 under the action of ZP, the deformation amount is 八1, A2. AP = Ki (Tx) A = K2(Tx)A2. is set in the MM direction of the common normal line. The deformation of the tooth profile 3, 4 is A4, and the meshing force is Pm. The component of Pm in the N-N direction of the meshing line is defined as the biting force Pni=by force. The balance and deformation harmonic conditions can be obtained as follows: 7屮8 1 Yao Wenxi, Wei Renzhi. The meshing impact response of the involute spur gear. Vibration, testing and diagnosis, 1992 Zhang Yongzhong, Wang Hong. About the test of the trimming gear. Gear, 1985, 9 (5): 12 ~ 15. Zhang Yongzhong. The process of grinding and shaping the spur gear. Coal Machinery 1984, (5): 14~16. Zhang Yongzhong. About the calculation method of the trimming gear. Coal machinery, 1984 Zhang Xikang. Calculation and processing of involute gear tooth tip trimming. Gear, 1985, 9 (6): 22 Wei Renzhi, Zhang Yongzhong, Shi Xinghong. Calculate the amount of deformation of the spur gear teeth. Gear, 1980, (4): 1 Xu Lizhong. The conformal mapping method accurately solves the deflection of the involute spur gear teeth. Journal of Mechanics, 1996, 32 (2): 14 (on page 4) Yao Wenxi, Wei Renzhi. Nonlinear vibration of involute spur gears. Journal of China University of Mining and Technology, 1989, (2):