Effect of Helix Angle on Dynamic Behaviors of Double Circular arc Helical Gears |
INTRODUCTION The double circular arc helical gears has advantage of high load capacity, uniform wear and easy forming hydrodynamic oil film between teeth etc，so it has been widely used in metallurgy machinery, mining machinery, petroleum and chemical machinery etc．industrial fields．In recent years，with the development of modem machinery toward direction of high running speed，heavy loading and small volume，the main obstacle conditioned this type of the helical gears further to be used is its dynamic behaviors such as vibration and noise．So it is necessary to study dynamic behaviors of the helical gear for further widening its application fields． The double circular arc helix angle gearing is an axial conjugate transmission that have several points contact at every instant．These sets of contact points in the fixed coordinate system form the line of action，which is a straight line that parallels to the gear axes．That is to say, there is only overlap ratio，and no transverse contact ratio during course of mating．The continuum mating among teeth is ensured mainly by overlap ratio．So this type of gearing has been manufactured to a helical gears，and helix angle has an important effect on dynamic transmitting behaviors of the helical gears． From the view point of studying results at present，as a main parameter in the helical gears design，the effectsof helix angle on transmitting behaviors of the gearing mainly acquit itself as follows： (1)with the increasing of helix angle，the mesh stiffness of a single pair of contact points is decdreased； (2)the overlap ratio of the helical gears is directly depended on the value of helix angle．From calculation formula of contact ratio of the helical gears, as keeping gear width and normal module on constants，increasing of helix angle causes the value of contact ratio，helix angle to increase；as keeping contact ratio and normal module on constants，increasing of helix angle causes helical gear width to decrease；meanwhile，from calculation formula of center distance of the helical gears，as keeping center distance，gear ratio，normal module on constants，increasing of helix angle causes the pinion’s tooth number and the meshing frequency to decrease at the same running speed，which is analogous to that the helical gears is running at low rotational speed． (3)the value of helix angle also has an effect on transmission error of the helical gears．As keeping error of helix angle on constant，increasing of helix angle can reduce the value of transmission error of the helical gears． In this paper, on condition that center distance．gear ratio，normal module，accuracy grade as well as transmitting torque of the helical gears are kept on constants，based on the single-degree-of-freedom dynamic model of the gears established in reference，in which the manufacturing errors，time-varying meshing stiffness，damping characteristic etc．are taken into account．an analysis has been carded out for studying the effect of helix angle on dynamic behaviors such as vibration acceleration，factor of dynamic load as well as natural vibration frequency of the gears system．In calculating process，using fourth order RUNGE-KUTTA method．a computer program has been developed by divided the meshing period into 100 iterative step length．the detail calculating process and methods can be found. 1 EFFECT OF HELⅨ ANGLE AND ROTATIONAL SPEED ON VIBRATIONACCELERATION AND FACTOR OF DYNAMIC LOAD The conclusions can be obtained as follows：on condition of the same ratio of critical rotational speed，increasing of helix angle cause the value of vibration acceleration and factor of dynamic load to reduce at most region of rotation speed，this tendency is especial prominence in region of higher rotational speed． The main reasons for the phenomena above are(1)I at the same value of contact ratio．increasing of helix angle causes the value of mesh stiffness of a single pair of contact points to reduce，which results in a slowly undulating tendency of changing scope of meshing stiffness；(2)at the same accuracy grade and tooth shape parameters，increasing of helix angle cause the value of transmission error to decrease．which also result in the displace excitement due to transmission error to reduce．Both of witch cause the vibration and dynamic load in transmission process to reduce. The calculated results are consistent with experimental results of the helical gears．on condition that the contact ratio equal to 1.15 and other parameters such as center distance，normal module etc．were kept on constants，a serial experiments about load capacity of the gears were carded out by changing the value of helix angle of the gears．The experiment could tell us that．in all of seven mid-size gear pairs of GB／T127591-1991 type used as tested examples．with the value of helix angle increasing，the noise due to vibration appears a distinct decreasing tendency． 2 EFFECT OF HELIX ANGLE AND CONTRACT RATIO ON DYNAMIC BEHAVIORS OF THE HELICAL GEARING For the purpose of comparing with the different effects between changing of helix angle and contact ratio on dynamic behavior of the helical gears，on condition that other calculated parameters are kept on constants．a comparative analysis about helix angle effecting on root-mean-square(r.m.s)of vibration acceleration and dynamic load factor of the gears was curried out by changing the value of helix angle corresponding to different contact ratio．From which we can coneluded that(1)decreasing scope of vibration due to increasing of helix angle is greater than that due to increasing of contact ratio；(2)augmentation of the value of helix angle and contact ratio simultaneously can obviously reduce vibration intensive of the helical gears． 3 EFFECT OF HELIX ANGLE ON NATURAL VIBRATION FREQUENCY OF THE GEARING SYSTEM The calculated formula of nature vibration freuency of the gearing system is(omit),Based on formula and the parameters of the helical gears．the state of nature vibration frequency of the gearing system varying with changing of helix angle is studied．The research result can be concluded that the value of nature vibration frequency of the gearing system is augment with the increasing of value of helix angle in its common use regionn; when the value of nature vibration frequency of the gearing system achieves a maximal value．however, its value appears a slowly decreasing tendency with further increasing of value of helix angle． Based on motioned above，in common use region of helix angle and rotational speed，On condition that other parameters are taken the same．increasing of the value of helix angle causes the number of tooth to reduce，which means that the meshing frequency to reduce，and the helical gears runs in a region of low rotational speed；on the other hand，increasing of the value of helix angle causes nature vibration frequency of the gearing system to augment．Thus，an apart tendency occurs between the value of the meshing frequency and that of nature vibration frequency of the gearing system，which leads intensive of vibration to reduce． 4 CONCLUSIONS Using numerical calculated method，the effect of helix angle on dynamic behaviors of double circular arc helical gears has been studied．It can be concluded from a series of different parametric studies presented here(1)On condition that the other parameters are taken the same，increasing of the values of helix angle causes the intensive of vibration and dynamic load of the helical gears to reduce．(2)Decreasing scope of vibration due to increasing of helix angle is greater than that due to increasing of contact ratio．(3) The value of nature vibration frequency of the gearing system is augment with the increasing of value of helix angle in its common use region．(4)Based on motioned above，under allowable condition，we suggest that the value of helix angle had better taken as large value as possible for the purpose of reducing the intensive of vibration．(Wu Baolin Xiao Fang School of Mechanical and Electronic Engineering，Tianjin Polytechnic University,China) |
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