Research On Improved Tooth Surface Modification Technology Based On Contact Ratio And Meshing Performance Of Involute Cylindrical Gears

Gear transmission is one of the most important components of machinery equipment,and its design and manufacturing technology represents the manufacturing level of a country to a certain extent.Involute cylindrical gears are widely used in industrical equipment because of their large bearing capacity and smooth transmission.Vibration and noise reduction through tooth surface modification play an important role in gear transmission design.With the development of industry,the speed and load of gears are getting higher and higher.Although the technology of vibration and noise reduction and gear tooth modification has been progressing,it is still far from meeting the requirements.For example,the reduction of vibration and noise of the high-speed aeronautical gears has always brought great troubles to engineers due to the high rotational speed;as another example,in the transmission system of the ship,especially in the power transmission of the submarine,the noise level of gear trasmission is far behind that of the advanced industrial countries,which has become an important obstacle to the development of the submarine technology of our country.Therefore,it is still of great practical significance to further study the tooth surface modification and meshing performance of the involute cylindrical gears.In this paper,it is determined that the loaded transmission error and the meshing impact are the main excitations in gear transmission through the excitation analysis.Under the back ground that the traditional tooth modification can not fully suit to the gears that the contact ratio is more than two which is widely used at present,and only to reduce the amplitude of the loaded transmission error is not suit to the high speed gears that working in the superresonance region,an improved design technology of the tooth modification of the involute cylindrical gears for vibration and noise reduction are proposed based on the high-precision modified tooth surface model and the tooth contact analysis and the loaded tooth contact analysis.Moreover,in-depth discussion and research are carried out.The main contents of this paper are as follows:1)Based on the high-precision modified tooth surface model and the tooth contact analysis and the loaded tooth contact analysis,an bias tooth modification method based on the contact ratio is proposed that the tooth modification is carried out through the predesignation of the geometrical transmission error of the modified tooth surface.In the proposed tooth modification method,in order to obtain the modified tooth surface with the minimum amplitude of the loaded transmission error,the preset geometrical transmission error of the modified tooth surface is designed to be equal in magnitude and oppsite in direction to the loaded transmission error of the standard involute gears under the design load.According to this idea,the amplitude of the loaded transmission error can be reduced to almost zero.2)Based on the tooth contact simulation,a simulation model of the tooth mesh-in contact considering the base pitch difference caused by load is established.The accurate position of the mesh-in point and the meshing stiffness of the mesh-in point and the relative velocity of the tooth surfaces considering the tooth modification and the base pitch difference at the mesh-in point are calculated,and finally,the meshing impact force is calculated;a contact simulation model that the contact between the tooth tip of gear and the tooth surface of pinion considering the base pitch difference under a large load is established.The accurate position of the mesh-in point and the meshing stiffness of the mesh-in point and the relative velocity of tooth surfaces considering the tooth modification and the base pitch difference at the mesh-in point are calculated,and finally,the mesh-in impact force is calculated.3)Based on the parametric modification tooth surface model and the tooth contact analysis,a multi-objective optimization model is established to reduce the amplitude of the loaded transmission error and the mesh-in impact force.The parameters of tooth surface modification are optimized and the designation of the tooth surface modification with the minimum amplitude of the loaded transmission error and the minimum mesh-in impact force is obtained.The dynamic model of gear transmission system is established and the dynamic analysis of gears under various modification conditions is carried out.On the one hand,the modification effect of the different modification methods is quantitatively compared and tested;on the other hand,the effect of the mesh-in impact force excitation and the loaded transmission error excitation on the vibration response of the gear transmission system is analyzed.4)The loaded transmission error and the mesh-in impact force of gears under different loads are calculated,and the influence of the loads on the amplitude of the loaded transmission error and the mesh-in impact force is analyzed.An equivalent load is obtained based on the middle-load and the most commonly used load of the load domain and the corresponding weight factor.The equivalent load is taken as the design load of the tooth surface modification,and the tooth surface is modified by the multi-objective optimization.Under the most commonly used load and most loads of the load domain,the amplitude of the loaded transmission error and the mesh-in impact force of the modified tooth surface is decreased greatly.An equivalent load is obtained based on the load spectrum and the probability of load appearing.The equivalent load is taken as the design load of the tooth surface modification.The tooth surface is modified by the multi-objective optimization.Under the most commonly used load and all the loads of the load spectrum,the amplitude of loaded transmission error and the mesh-in impact force of the modified gears is decreased considerably.5)According to the standard tooth surface and the traditional tooth modification theory and the improved tooth modification theory,the involute cylindrical gears for testing are designed and processed.The testing of the accuracy of the tooth surface processing is carried out.Furthermore,the tooth surface rolling is carried out to verify the simulation of the geometrical contact of the modified gears.Moreover,the test gears are installed on the closed test bench of the cylindrical gears.The transmission error of the gears and the vibration acceleration of the gearbox body is measured under different loads to verify the improved tooth modification theory and the design technology.