JP4916761B2 - Dynamic analysis method of rolling bearing under planetary motion - Google Patents

Description

  The present invention relates to a dynamic analysis method for a rolling bearing that supports a planetary gear under planetary motion.

The planetary gear mechanism has a structure in which several planetary gears are meshed with one input gear, the transmission torque is once shared, and these are concentrated again into one output gear. The transmission torque is extremely high and is used in many transmissions (for example, Non-Patent Document 1).
In addition, rolling bearings are used as support bearings for planetary gears that make planetary motions in order to reduce vibration and noise and increase transmission efficiency. However, in rolling bearings under planetary motion, cage breakage may become a problem.

The planetary gear is subjected to an interference force from the two sun gears (external gear sun gear, internal gear) via the tooth surface and a dynamic load due to the movement of the carrier. Although there are analysis examples of the interference force itself on these tooth surfaces (for example, Non-Patent Document 2), no motion analysis of the planetary gear support bearings is found.
Written by Akira Waguri, “Gear Design / Manufacturing and Its Durability”, published in 1980, Yokendo, P197-200 Shigeki Muramatsu et al., “Prediction of meshing non-integer order vibrations by tooth surface measurement”, Proceedings of the 1st Lecture on Basic Lubrication Division of the Japan Opportunity Association, 2001, P63-64 Sakaguchi & Ueno, “Cylinder roller bearing cage behavior analysis”, NTN TECHNICAL REVIEW, No71, 2003, 8-17

In order to clarify the problem of cage breakage in planetary gear support bearings, numerical analysis of rolling bearing dynamics is effective. The dynamic analysis of the rolling bearing can be performed on commercially available general-purpose mechanism analysis software, for example, and has been put into practical use (for example, Non-Patent Document 3). This uses a two-dimensional dynamic analysis model of a rolling bearing that takes into account three degrees of freedom of rollers and cages and two degrees of freedom of translation of the outer ring.
However, as described above, the load history acting on the planetary gear is complicated, and it is difficult to construct a dynamic analysis model of the rolling bearing including the entire planetary gear mechanism.

  The object of the present invention is to enable dynamic analysis of rolling bearings under planetary motion relatively easily, and to perform rolling under planetary motions that can contribute to elucidating the quality problems of various rolling bearing parts represented by cage breakage. It is to provide a dynamic analysis method for bearings.

The dynamic analysis method for a rolling bearing under planetary motion according to the present invention proposes a practical rolling bearing dynamic analysis model that simplifies the load acting on the planetary gear.
That is, the dynamic analysis method for a rolling bearing under planetary motion according to the present invention is the planetary gear mechanism in which the planetary gear meshing with the external sun gear and the internal gear is rotatably supported by the carrier via the rolling bearing. In a method for performing dynamic analysis of a rolling bearing,
As a dynamic analysis model of the planetary gear mechanism, the degree of freedom of movement of the components of the planetary gear mechanism is limited to a radial plane, the angular speed of the planetary gear rotation and the carrier rotation is constant, and the carrier and external teeth A model in which the center position of the sun gear is fixed to the center of the internal gear is used. For this dynamic analysis model, by expressing the transmission torque of the planetary gear mechanism revolving radial load of the planetary gear, e given a planetary gear mechanism of the specific load applied to the rolling bearing in simulated, and the In the model, the load specific to the planetary gear mechanism acting on the rolling bearing is expressed by the following (Assumption 1) to (Assumption 7) .
(Assumption 1) Consider the inertial force and centrifugal force of the parts subject to dynamic analysis.
(Assumption 2) The mutual contact force and tangential force of the rolling elements, cage, shaft, and planetary gear of the rolling bearing are taken into consideration.
(Assumption 3) The rotational angular velocities of the carrier and the planetary gear are given as constant conditions or known conditions such as a known function. Therefore, the revolution angular velocity of the planetary gear is defined as the degree of freedom in dynamic analysis.
(Assumption 4) The center positions of the external sun gear, the internal gear, and the carrier are fixed and coincide with each other.
(Assumption 5) Since the meshing clearance of the tooth surface contact portion between the planetary gear, the external sun gear, and the internal gear is larger than the radial internal clearance of the rolling bearing that supports the planetary gear, the planetary gear corresponding to the radial internal clearance is provided. Gives two translational degrees of freedom.
(Assumption 6) The interference force from the internal gear and the external sun gear to the planetary gear can be reduced to the translational force and the rotation moment in the revolution direction of the planetary gear. Further, under the steady operation state, this translational force is determined by the transmission torque.
(Assumption 7) Three degrees of freedom of rotation and two translations are given to the cage and rolling elements of the rolling bearing.

According to this dynamic analysis method, the load acting on the complex planetary gear unique to the planetary gear mechanism can be simplified. Therefore, the two-dimensional rolling bearing considering the three degrees of freedom of the rollers and the cage and the two degrees of freedom of translation of the outer ring. by using dynamic analysis models, dynamic analysis of the rolling bearing of the lower planetary motion becomes easily feasible. Therefore, Ru can contribute to the elucidation of quality problems of the various rolling bearings components typified by cage damage.
By the above (Assumption 6), the nominal radial load in the revolution direction of the planetary gear can be set. This radial load will determine the dynamic behavior of the rolling elements and cage.

  In the present invention, the dynamic analysis model may be one in which the angular speeds of the planetary gear rotation and the carrier rotation are known functions. That is, a known function may be used instead of making the angular speeds of the planetary gear rotation and the carrier rotation constant. If it is a known function, the dynamic analysis of the rolling bearing can be performed with higher accuracy.

  The rolling bearing may be, for example, a roller with a cage in which an outer diameter surface of a shaft fixed integrally with a carrier and an inner diameter surface of a planetary gear serve as a bearing raceway surface on which a rolling element rolls.

The dynamic analysis method for a rolling bearing under planetary motion according to the present invention is a dynamic analysis model for a planetary gear mechanism, in which the degree of freedom of movement of the components of the planetary gear mechanism is limited to a radial plane, and And the rotation speed of the carrier is constant, and the center position of the carrier and external sun gear is fixed at the center of the internal gear. This is a method of simulating the load specific to the planetary gear mechanism acting on the rolling bearing by expressing it by the revolution radial load of the gear , and in order to express the model by the above (Assumption 1) to (Assumption 7) Rolling under planetary motion by using the dynamic analysis technology of the rolling bearing using the two-dimensional dynamic analysis model of the rolling bearing considering the 3 degrees of freedom of the cage and the 2 degrees of freedom of translation of the outer ring. Dynamic analysis of the bearing becomes relatively easy to be implemented, it is possible to contribute to the elucidation of the cage various rolling components quality problems typified breakage.

  An embodiment of the present invention will be described with reference to FIGS. FIG. 1 shows the outline of the planetary gear mechanism in the radial direction. In this planetary gear mechanism, a plurality of (for example, 3 to 5) planetary gears 1 are engaged with the externally toothed sun gear 3 and the internal gear 2, and each planetary gear 1 is a rolling bearing on the outer periphery of the shaft 4 integral with the carrier 7. 9 is supported rotatably through 9. The o-xy coordinate system of FIG. 1 is fixed to the center of the shaft 4 that is integral with the carrier 7.

  The rolling bearing 9 is a roller with a cage in which a plurality of rolling elements 5 are held by a ring-shaped cage 6, and the outer diameter surface of the shaft 4 and the inner diameter surface of the planetary gear 1 are in rolling contact with each rolling element 5. It becomes a raceway surface. The cage 6 has pockets 6a at a plurality of locations in the circumferential direction, and holds the rolling elements 5 in the pockets 6a. The rolling element 5 includes rollers such as needle rollers.

Next, a dynamic analysis method for the rolling bearing 9 incorporated in the planetary gear mechanism will be described. In order to elucidate the interference force with the cage 6 in the rolling bearing 9 which is a support bearing of the planetary gear 1, dynamic analysis of the rolling bearing 9 capable of simulating dynamic behavior is required.
In this embodiment, in order to make it a category of a practical dynamic analysis model, as the dynamic analysis model of the planetary gear mechanism in FIG. 1, only the degrees of freedom in the radial plane with respect to the degrees of freedom of each component of the planetary gear mechanism. A model is used for. In this model, the load peculiar to the planetary gear mechanism acting on the rolling bearing 9 is expressed by the following assumptions.

(Assumption 1) Consider the inertial force and centrifugal force of the parts subject to dynamic analysis.
(Assumption 2) The mutual contact force and tangential force of the rolling element 5, the cage 6, the shaft 4, and the planetary gear 1 are considered.
(Assumption 3) The rotational angular velocities of the carrier 7 and the planetary gear 1 are given as constant or known conditions such as a known function. Therefore, the revolution angular velocity of the planetary gear 1 is set as the degree of freedom of dynamic analysis.
(Assumption 4) The center positions of the external gear sun gear 3, the internal gear 2 and the carrier 7 are fixed and coincide with each other at O in FIG.
(Assumption 5) Since the meshing clearance of the tooth surface contact portion between the planetary gear 1 and the external sun gear 3 and the internal gear 2 is larger than the radial internal clearance of the rolling bearing 9 that supports the planetary gear 1, Two degrees of freedom of translation of the planetary gear 1 for the gap (directions x and y in FIG. 1) are given.
(Assumption 6) The interference force from the internal gear 2 and the external sun gear 3 to the planetary gear 1 can be reduced to the translational force Ft and the rotation moment of the planetary gear 1 in the revolution direction (x direction in FIG. 1). Furthermore, this translational force is determined by the transmission torque Mt under steady operating conditions.
(Assumption 7) The cage 6 and the rolling element 5 of the rolling bearing 9 are given three degrees of freedom of rotation and two translations.

  Based on the above assumptions, the equation of motion of each motion analysis component is expressed by equations (1) to (5). In addition, due to the formulation in the inertial system, the centrifugal force that is an apparent force does not appear.

However, each symbol is as follows.
F: interference force, I: moment of inertia, i: rolling element number, m: mass, M: moment, Fa: interference force from carrier to rolling element, r: position vector, θ: angular displacement.
For subscripts, a: carrier, ab: component from carrier to rolling element, ac: component from carrier to cage, b: rolling element, c: cage, cb: cage to rolling element Component, p: planetary gear, pb: component from planetary gear to rolling element, pc: component from planetary gear to cage, t: resultant component of interference force from external sun gear and internal gear to planetary gear It is a component determined by the transmission torque under steady state.
Further, the bold character indicates a vector.

  With the assumption 6, the nominal radial load in the revolution (x in FIG. 1) direction of the planetary gear 1 can be set. This radial load determines the dynamic behavior of the rolling elements 5 and the cage 6.

  In the above equations of motion (1) to (5), Ft in equation (5) is determined by the rotational torque transmitted to the carrier 7. In addition, since the rotation speed of the planetary gear and the rotation speed of the carrier are given, the interference force and moment force between the components of these equations and the centrifugal force acting on each component are expressed by the equation of motion as in Non-Patent Document 3. All are obtained by numerical integration.

Since the magnitude of the interference force acting on the planetary gear 1 via the tooth surface changes depending on the meshing of the teeth, it is easy to handle if given as a function based on the rotation angle of the gear. For further simplification, a constant value may be used regardless of time.
Usually, there are a plurality of planetary gears in the planetary gear mechanism, but assuming that all are equivalent, one of them may be analyzed ignoring gravity. This is a reasonable assumption especially when the planetary gear has a high revolution speed and the centrifugal acceleration is greater than the gravitational acceleration.

  FIG. 3 shows a planetary gear mechanism serving as a planetary transmission having a reversing mechanism in which two sets of planetary gears are incorporated. When analyzing such a planetary gear mechanism, if the object to be analyzed is the planetary gear 1, the direction of the resultant vector of the interference force from the external gear 3 acting on the planetary gear 1 and the interference force from the other planetary gear 8 will be described. Is considered as a radial load on the planetary gear 1. Thereby, analysis is possible in the same manner as in the planetary gear mechanism of FIG. Even in this case, the magnitude of the moment to the carrier 7 due to the radial load may be set so as to balance the magnitude of the transmission torque.

It is a fragmentary front view of the planetary gear mechanism used as the analysis object in one embodiment of this invention. It is a fragmentary sectional view showing an example of the rolling bearing for supporting the planetary gear in the planetary gear mechanism. It is a partial front view of the planetary gear mechanism with the inversion mechanism used as the analysis object in other embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Planetary gear 2 ... Internal gear 3 ... External-tooth sun gear 4 ... Planetary gear shaft 5 ... Rolling element 6 ... Cage 7 ... Carrier 8 ... Planet gear for reversal

Claims (3)

In the planetary gear mechanism in which the planetary gear meshing with the external sun gear and the internal gear is rotatably supported on the carrier via the rolling bearing, in the method of performing dynamic analysis of the rolling bearing,
As a dynamic analysis model of the planetary gear mechanism, the degree of freedom of movement of the components of the planetary gear mechanism is limited to a radial plane, the angular speed of the planetary gear rotation and the carrier rotation is constant, and the carrier and external teeth Using a model in which the center position of the sun gear is fixed to the center of the internal gear, the transmission torque of the planetary gear mechanism is expressed by the radial radial load of the planetary gear for this dynamic analysis model. for example given a planetary gear mechanism of the specific load applied to the bearings simulated, and in the model, it loads specific to the planetary gear mechanism which acts on the rolling bearing, expressed by the following (assuming 1) to (assuming 7) dynamic analysis how the rolling bearing under planetary motion, characterized in that shall be.
(Assumption 1) Consider the inertial force and centrifugal force of the parts subject to dynamic analysis.
(Assumption 2) The mutual contact force and tangential force of the rolling elements, cage, shaft, and planetary gear of the rolling bearing are taken into consideration.
(Assumption 3) The rotational angular velocities of the carrier and the planetary gear are given as constant conditions or known conditions such as a known function. Therefore, the revolution angular velocity of the planetary gear is defined as the degree of freedom in dynamic analysis.
(Assumption 4) The center positions of the external sun gear, the internal gear, and the carrier are fixed and coincide with each other.
(Assumption 5) Since the meshing clearance of the tooth surface contact portion between the planetary gear, the external sun gear, and the internal gear is larger than the radial internal clearance of the rolling bearing that supports the planetary gear, the planetary gear corresponding to the radial internal clearance is provided. Gives two translational degrees of freedom.
(Assumption 6) The interference force from the internal gear and the external sun gear to the planetary gear can be reduced to the translational force and the rotation moment in the revolution direction of the planetary gear. Further, under the steady operation state, this translational force is determined by the transmission torque.
(Assumption 7) Three degrees of freedom of rotation and two translations are given to the cage and rolling elements of the rolling bearing.   2. The dynamic analysis method for a rolling bearing under planetary motion according to claim 1, wherein the dynamic analysis model is a planetary gear rotation and a carrier rotation angular velocity having a known function.   3. The roller bearing according to claim 1, wherein the rolling bearing is a roller with a cage in which an outer diameter surface of a shaft fixed integrally with a carrier and an inner diameter surface of a planetary gear serve as a bearing raceway surface on which a rolling element rolls. Dynamic analysis method for rolling bearings in motion.

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