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Abstract

Double-row planetary gear set (PGS) is a common form of the PGS, which is relatively more complex than the regular PGSs. It consists of one sun gear, several long planets, several short planets, two ring gears, and one carrier. Due to the significantly wider tooth width of the long planet compared to the sun gear, the axial meshing position between the sun gear and the long planet can be adjusted. The vibrations of PGS should vary with different axial meshing positions. If the axial position of the sun gear is optimized, the vibrations of PGS can be reduced. This work establishes a dynamic model of a double-row PGS. The dynamic model considers the mesh forces of the gear pairs and the supporting forces of the bearing. The effect of the sun gear axial position on the sun gear and ring gear #2 vibrations are investigated. Finally, the recommended axial position for the sun gear is provided.

Keywords

Double-row planetary gear set dynamic model vibration analysis axial position

Introduction

Planetary gear set (PGS) is widely used in various transmission mechanisms. Due to different requirements, the PSG is usually designed in various structural forms. Double-row PGS (double-ring Ravigneaux PSG) is a common form that is relatively more complex than the regular PGS.¹ It utilizes a long planet to transmit power. The sun gear tooth width and the long planet tooth width have a significant difference. The excessive vibration may cause some fails in the double-row PGS, which will affect its reliability and operational stability.² The axial position of the sun gear has a significant effect on the vibrations of the double-row PGS. Thus, it is essential to establish the double-row PGS dynamic model and investigate the effect of the sun gear axial position on the vibrations of the double-row PGS.

The study methods for the double-row PGSs are similar to those for the PSGs. Many works^3–15 have been conducted in the PGS dynamic modeling methods. Liu et al.^16,17 established a dynamic model for a double PGS and investigated its vibrations. In their work, the planetary bearings were completely modeled. Li et al.¹⁸ investigated the effect of the planetary bearing ring wear on the double PGS vibrations. The ring wear was the time-varying; and it was regarded as bearing clearance. Shen et al.¹⁹ proposed a dynamic model for the PGS with the gear wear. They considered the effect of the gear wear on the meshing stiffness and the meshing deformation by regarding the gear wear as the gear backlash. Xiang et al.²⁰ investigated the vibrations of a multistage planetary gear system with the gear tooth spalling. The effect of the gear tooth spalling on the time-varying meshing stiffness was considered. Ryali and Talbot²¹ proposed an improved dynamic load distribution model of a PGS, which was not needed to calculate the mesh stiffness and transmission error. Chen et al.²² studied the effect of the sun gear tooth crack on the vibrations of the PGS with the bearing clearance. Lai et al.²³ established a dynamic model for the PGS with a floating ring gear. The rotational DOF was free in their work. Zhang et al.²⁴ established a dynamic model for the PGS with the journal bearing and studied the effect of the journal bearing error on the PGS load-sharing characteristics. The flexibility of the ring gear was considered by using the Euler Bernoulli beam element. Pfeiffer²⁵ studied the dynamics of a Ravigneaux PSG. Liu et al.²⁶ proposed a PGS dynamic model considering the flexible ring and carrier. Moreover, the electric motor torque fluctuation is considered in their work. Mo et al.²⁷ established a dynamic model for a PGS with the flexible support and floating sun gear. Based on the dynamic model, they studied the PGS vibrations and load-sharing characteristics. Yang et al.²⁸ analyzed the effects of the cyclic load and random wind load on the vibrations of the PGS in the wind turbines. However, they only considered the torsional vibrations of the PGS. Westphal et al.²⁹ investigated the effects of the axis misalignments on the PGS vibrations based on an experimental method. Wang et al.³⁰ studied the vibrations of a PGS with thin-walled ring gear considering the ring gear flexibility. In their work, the planetary bearing was regarded as a spring-damping system and the bearing nonlinear characteristics were ignored. Zhang et al.³¹ established a rigid-flexible coupling dynamics model for the planetary gearbox and analyzed the fault mechanism for the PGS under speed-varying conditions. The planetary bearing nonlinear characteristics were also ignored. Dai et al.³² investigated the mesh phasing modulation of PGS caused by position errors. The simulation results were compared with the experimental results to validate the correctness of the proposed model. It should be noted that although the research subjects in references [2,15,24] are double-ring Ravigneaux PSG, they did not study the effect of sun gear axial position on it's vibrations.

Based on the above literature review, it can be observed that most previous works focused on the conventional PGSs, which consist of one sun gear, several planets, one ring gear, and one carrier. Few works have been conducted on the vibrations of the double-row PGSs, which consists of one sun gear, several long planets, several short planets, two ring gears, and one carrier. Furthermore, due to the significantly wider tooth width of the long planet compared to the sun gear, the axial meshing position between the sun gear and the long planet can be adjusted. The vibrations of the PGS vary with different axial meshing positions. The excessive vibration can affect the normal operation of the double-row PGS; and it can also impact the operation of other parts connected to the double-row PGS.³³ By optimizing the axial position of the sun gear, the vibrations of the PGS can be reduced. Therefore, this work establishes a dynamic model for the double-row PGS and studies the effect of the sun gear axial position on the vibrations of PGS. The effect of the sun gear axial position on the vibrations of the double-row PGS under two typical operating conditions are investigated. Moreover, a vibration suppression method is proposed to guide the double-row PGS actual operation.

Problem description

Figure 1 shows the schematic diagram of the studied double-row PGS in this work. The double-row PGS consists of one sun gear, one carrier, one short planet, one long planet, and two ring gears. The rotational degree of freedom (DOF) of the sun gear is constrained and ring gear #1 is floating. The ring gear #2 is the input component and the carrier is the output component. The tooth width of the long planet is larger than the one of the sun gear. Generally, the symmetry plane of the sun gear and the planet in the direction of tooth width coincides. However, the meshing force between the long planet and ring gear, as well as that between the long planet and short planet, may not be equal. When the symmetry plane of the sun gear and the planet in the direction of tooth width coincide, the meshing forces will generate an overturning moment, which affects the stability and vibrations of the double-row PGS. On the other hand, an appropriate axial position of the sun gear can enhance the stability and reduce vibrations of the double-row PGS.

Figure 1.

Schematic diagram of the double-row PGS. (a) Front view and (b) A–A section view. PGS: planetary gear set.

It is assumed that the sun gear is rotationally fixed and can only be moved axially by the amount A_z. Then the double-row PGS has two drive transfer paths. The first drive transfer path is ring gear #2–long planet–carrier or in the opposite direction. When ring gear #2 is the input element, carrier is the output element, sun gear is fixed, and ring gear #1 is the free element, then the DOF of such a system is

M_{(1)} = 3 n_{(1)} - 2 p_{5 (1)} - p_{4 (1)} = 3 \times 3 - 2 \times 3 - 2 = 1

(1)where n₍₁₎ is the active element number (ring gear #2, long planet, and carrier), the free and fixed elements (ring gear #1, short planet, and sun gear) have been omitted; p₅₍₁₎ the number of rotating pairs of ring gear #2, long planet and carrier bearings; p₄₍₁₎ the number of meshing pairs (ring gear #2–long planet and long planet–sun gear) without considering the meshing pair of the free elements (long planet–short planet and short planet–ring gear #1).

The gear ratio is

i_{(1)} = \frac{n_{r 2}}{n_{c}} = 1 - \frac{Z_{s}}{Z_{r 2}} = 1.442

(2)where n_c and n_r₂ are the carrier rotational speed and ring gear #2 rotational speed; Z_r₂ and Z_s are the ring gear #2 tooth number and sun gear tooth number.

The second drive transfer path is ring gear #1–short planet–long planet–carrier or in the opposite direction. When ring gear #1 is the input element, carrier is the output element, sun gear is fixed, and ring gear #2 is free element, then the DOF of such a system is

M_{(2)} = 3 n_{(2)} - 2 p_{5 (2)} - p_{4 (2)} = 3 \times 4 - 2 \times 4 - 3 = 1

(3)where n₍₂₎ is the active element number (ring gear #1, short planet, long planet, and carrier), the free and fixed elements (ring gear #2 and sun gear) have been omitted; p₅₍₂₎ the number of rotating pairs of ring gear #1, short planet, long planet, and carrier bearings; p₄₍₂₎ the number of meshing pairs (ring gear #1–short planet, short planet–long planet, and long planet–sun gear) without considering the meshing pair of the free elements (long planet–ring gear #2).

The gear ratio is

i_{(1)} = \frac{n_{r 1}}{n_{c}} = 1 - \frac{Z_{s}}{Z_{r 1}} = 1.415

(4)where n_r₁ is the ring gear #1 rotational speed and Z_r₁ the ring gear #1 tooth number.

It should be noted that the first drive transfer path is ring gear #2–long planet–carrier is the studied case in this work.

Double-row PGS modeling

Double-row PGS dynamic modeling

The double-row PGS dynamic model is shown in Figure 2, which is established in SIMPACK software. The double-row PGS consists of a sun gear, three short planets, three long planets, and two ring gears. The ring gear #2 is connecting with the input shaft. The input torque is applied to the ring gear #2. The carrier is connected to the output shaft and the output torque is applied to the carrier. The rotational motion of the carrier is free. The rotational motion of the sun gear is constrained, but the sun gear is floating in z direction. Moreover, the ring gear #1 is floating (the rotational motion is free). The gear meshing pair is modeled by the #225: the gear Pair force element, the relevant method is given in the Double-row PGS dynamic modeling section. By varying the axial coordinates of the sun gear joint, the effect of the sun gear axial position on the double-row PGS vibrations can be studied. It should be noted that the planets are supported by the cylindrical roller bearings (CRBs) and the other components are supported by the deep groove ball bearings (DGBs). In this work, A_z is adapted to describe the sun gear position, as shown in Figure 1.

Figure 2.

A double-row PGS dynamic model. PGS: planetary gear set.

Gear meshing force calculation method

The gear tooth geometry is shown in Figure 3. Based on the Weber–Banaschek formula, the mesh stiffness is calculated by the following equation³⁴

δ_{Z} = \frac{F_{N}}{E_{b}} \cos^{2} α_{x} [10.92 \int_{0}^{h_{x}} \frac{{(h_{x} - y)}^{2}}{{(2 x)}^{3}} d y + 3.1 (1 + 0.294 \tan^{2} α_{x}) \int_{0}^{h_{x}} \frac{d y}{2 x}]

(7)

δ_{R} = \frac{F_{N}}{E_{b}} \cos^{2} α_{x} [5.2 \frac{h_{x}^{2}}{S_{F}^{2}} + \frac{h_{x}}{S_{F}} + 1.4 (1 + 0.294 \tan^{2} α_{x})]

(8)where x and y are the coordinates of the meshing force action point, α_x the mesh angle, F_N the meshing force, E_b and b the comprehensive elastic modulus and tooth width, and h_x and S_F shown in Figure 3.

δ_{pW} = 0.58 \frac{F_{N}}{E_{b}} (\ln \frac{2 h_{1}}{a} + \ln \frac{2 h_{2}}{a} - 0.429)

(9)

a = 1.52 \sqrt{\frac{F_{N}}{E_{b}}} \sqrt{\frac{ρ_{1} ρ_{2}}{ρ_{1} + ρ_{2}}}

(10)

δ_{Σ} = δ_{Z 1} + δ_{Z 2} + δ_{R 1} + δ_{R 2} + δ_{p W}

(11)

k = \frac{F_{N}}{δ_{Σ}}

(12)where k is the mesh stiffness, and ρ₁ and ρ₂ the curvature radius of driving gear and driven gear on the mesh point.

Figure 3.

Gear tooth geometry parameters in Weber–Banaschek formula.

Then, the meshing force can be given by

F_{N} = k δ + c \dot{δ}

(13)where δ is the mesh deformation and c the mesh damping coefficient. Their calculation method can be found in reference [16].

Bearing supporting force

The bearing contact force of the DGB is calculated by

F_{c j} = c_{p} δ_{j}^{\frac{3}{2}}

(14)where δ_j is bearing contact deformation and c_p the bearing comprehensive contact stiffness, which is^35–37

c_{p} = {[\frac{1}{{(1 / K_{i})}^{\frac{2}{3}} + {(1 / K_{o})}^{\frac{2}{3}}}]}^{1.5}

(15)where K_i and K_o are the contact stiffnesses between the ball and inner/outer ring, and their calculation method can be found in reference [10].

As shown in Figure 4, the contact deformation between the ball and bearing ring δ_j is

δ_{j} = (δ_{r, j} - s_{r}) \cos (α_{j}) + (δ_{a, j} - s_{a}) \sin (α_{j})

(16)where, δ_r and δ_a are the displacements in radial and axial directions; s_r and s_a the bearing radial and axial clearances.

Figure 4.

Schematic of the bearing deformation.

The bearing supporting force is calculated by

F_{b} = \sum_{j = 1}^{Z} F_{c j}

(17)where Z is the number of bearing roller element.

The bearing contact force of the CRB is

F_{c j} = c_{s} δ_{j}^{\frac{10}{9}}

(18)where c_s is the contact stiffness between the roller and bearing ring, which is

c_{s} = \frac{35948 L_{w}^{\frac{8}{9}}}{n_{s}}

(19)where, L_w is the roller effective length.

Results and discussions

In this work, the effect of the sun gear axial position on the double-row PGS vibrations under two operating conditions is investigated. The operating conditions are presented in Table 1. The gear structural parameters of the double-row PGS are given in Table 2; and the bearing structural parameters are given in Table 3.

Table 1.

The operating condition parameters.

Operating condition	Input speed	Input torque	Output speed	Output torque
1	78.32 rad/s	27,033.9 N·m	54.33 rad/s	38,970.6 N·m
2	243.99 rad/s	3772.5 N·m	169.26 rad/s	5438.18 N·m

Table 2.

Structural parameters of the double-row planetary gear set.

Parameters	Sun gear	Long planet	Short planet	Ring gear #1	Ring gear #2	Carrier
Module (mm)	4	4	4	4	4
Teeth number	34	21	22	82	77
Tooth width (mm)	41	78	40	65	40
Pressure angle (°)	25	25	25	25	25
Mass (kg)	3.6	2.4	1.4	7.7	7.2	34
Moment of inertia (kg·mm²)	600	2638	1033	104,318	111,934	286,339

Table 3.

Bearing structural parameters.

Parameters	Long planetary bearing	Short planetary bearing	else
Type	CRB	CRB	DGB
Rolling element number	22	22	22
Pitch diameter (mm)	42	42	170.034
Rolling element diameter (mm)	2	2	12.712
Inner ring groove radius (mm)	—	—	6.612
Outer ring groove radius (mm)	—	—	6.738

CRB: cylindrical roller bearing; DGB: deep groove ball bearing.

Time-varying mesh stiffness analysis

The time-varying mesh stiffnesses of the double-row PSG are given in Figure 5. The rotational speed of ring #2 is 78.32 rad/s, the rotational speed of long planet is 138.29 rad/s, and the rotational speed of carrier is 54.33 rad/s. The meshing period of sun gear-long planet mesh pair is 0.00356 s; the meshing period of long–short planets mesh pair is 0.003402 s; and the meshing period of long planet–ring gear mesh pair is 0.003401 s. The time-varying mesh stiffness of the sun gear-long planet mesh pair maximum (MAX) value is 1.355 × 10⁹ N/m; and its minimum (MIN) value is 7.318 × 10⁸ N/m. The time-varying mesh stiffness of long-short planets mesh pair MAX value is 1.528 × 10⁹ N/m and its MIN value is 8.658 × 10⁸ N/m. The time-varying mesh stiffness of short planet–ring gear mesh pair MAX value is 1.995 × 10⁹ N/m and its MIN value is 1.144 × 10⁸ N/m.

Figure 5.

Time-varying mesh stiffness of the (a) sun gear-long planet mesh pair, (b) long–short planets mesh pair, and (c) long planet-ring gear mesh pair.

Time-domain vibrations of the double-row PGS

Figure 6 shows the ring gear #2 angular accelerations, ring gear #2 accelerations in x direction, and sun gear accelerations in z direction under operating condition 1. The root mean square (RMS) value of ring gear #2 angular accelerations is 1508.33 rad/s² and its peak-to-peak (PTP) value is 1.278 × 10⁴ rad/s². The RMS value of ring gear #2 accelerations in x direction is 258.462 m/s² and its PTP value is 2.213 × 10³ m/s². The RMS value of sun gear accelerations in z direction is 151.59 m/s² and its PTP value is 1226.09 m/s².

Figure 6.

Time-domain vibrations of the double-row PGS under operating condition 1. (a) The ring gear #2 angular accelerations, (b) ring gear #2 accelerations in x direction, (c) sun gear accelerations in z direction, and (d) ring gear #2 accelerations spectrum in x direction. PGS: planetary gear set.

Figure 7 shows the ring gear #2 angular accelerations, ring gear #2 accelerations in x direction, and sun gear accelerations in z direction under operating condition 2. The RMS value of ring gear #2 angular accelerations is 1.217 × 10³ rad/s² and its PTP value is 8.854 × 10³ rad/s². The RMS value of ring gear #2 accelerations in x direction is 117.647 m/s² and its PTP value is 1.413 × 10³ m/s². The RMS value of sun gear accelerations in z direction is 116.43 m/s² and its PTP value is 841.46 m/s².

Figure 7.

Time-domain vibrations of the double-row PGS under operating condition 2. (a) The ring gear #2 angular accelerations, (b) ring gear #2 accelerations in x direction, (c) sun gear accelerations in z direction, and (d) ring gear #2 accelerations spectrum in x direction. PGS: planetary gear set.

Effect of the sun gear axial position on its own vibrations

The effect of the sun gear axial position on its own vibrations under operating condition 1 is plotted in Figure 8. Figure 8(a) shows the effect of the sun gear axial position on the RMS values of its own vibrations. The RMS value of the sun gear vibrations in z direction generally decreases with the increment of the A_z. Moreover, the RMS value decreases dramatically when A_z = 6 mm. Figure 8(b) shows the effect of the sun gear axial position on the PTP values of its own vibrations. The PTP value of the sun gear vibrations in z direction generally decreases with the increment of the A_z. Moreover, the PTP value also decreases dramatically when A_z = 6 mm. It can be found that the change pattern of the PTP value with A_z is consistent with the one of the RMS value with A_z.

Figure 8.

Effect of the sun gear axial position on its own vibration in z direction under operating condition 1.

Furthermore, when A_z is <6 mm, the sun gear axial position has a significant effect on the sun gear vibrations. As A_z increases, the RMS and PTP values of sun gear vibrations decrease dramatically. However, when A_z is larger than 6 mm, the sun gear axial position has a minor effect on the sun gear vibrations.

The effect of the sun gear axial position on its own vibrations under operating condition 2 is plotted in Figure 9. Figure 9(a) shows the effect of the sun gear axial position on the RMS values of its own vibrations. The RMS value of the sun gear vibrations in z direction decreases with the increment of the A_z. Figure 9(b) shows the effect of the sun gear axial position on the PTP values of its own vibrations. The PTP value of the sun gear vibrations in y direction generally decreases with the increment of the A_z. The PTP value of the sun gear vibrations in x direction generally decreases with the increment of the A_z. Similar to the results under operating condition 1, the PTP value also decreases dramatically when A_z= 6 mm.

Figure 9.

Effect of the sun gear axial position on its own vibration in z direction under operating condition 2.

Furthermore, the sun gear axial position has a relatively significant effect on the sun gear vibrations when A_z is <6 mm, which is similar to the results under operating condition 1. The difference is that the axil position still has a relatively significant effect on the sun gear RMS value when A_z is larger than 6 mm.

Effect of the sun gear axial position on the ring gear #2 vibrations

The effect of the sun gear axial position on the ring gear #2 vibrations under the operating condition 1 is plotted in Figure 10. Figure 10(a) shows the effect of the sun gear axial position on the RMS values of the ring gear #2 angular accelerations. The RMS value decreases with the increment of A_z when A_z is <18 mm; and the RMS value increases with the increment of A_z when A_z is larger than 18 mm. Moreover, the sun gear position has a relatively significant effect on the angular accelerations RMS value of the ring gear #2 when A_z is <18 mm. Figure 10(b) shows the effect of the sun gear axial position on the PTP values of the ring gear #2 angular accelerations. The PTP value generally decreases with the increment of A_z when A_z is <18 mm; and the PTP value generally increases with the increment of A_z when A_z is larger than 18 mm. Figure 10(c) shows the effect of the sun gear axial position on the RMS values of the ring gear #2 accelerations in x directions. The RMS value generally decreases with the increment of A_z. The sun gear position has a relatively significant effect on the acceleration RMS value of the ring gear #2 in y direction when A_z is <18 mm; and the RMS value decreases significantly when A_z is <18 mm. Figure 10(d) shows the effect of the sun gear axial position on the PTP values of the ring gear #2 accelerations in x directions. The PTP value generally decreases with the increment of A_z; and it only has an increment when A_z= 18 mm.

Figure 10.

Effect of the sun gear axial position on the ring gear #2 vibrations under operating condition 1. (a) The RMS values of the ring gear angular acceleration, (b) PTP values of the ring gear angular acceleration, (c) RMS values of the ring gear acceleration in x direction, and (d) PTP values of the ring gear acceleration in x direction. PTP: peak-to-peak; RMS: root mean square.

The effect of the sun gear axial position on the ring gear #2 vibrations under the operating condition 2 is plotted in Figure 11. Figure 11(a) shows the effect of the sun gear axial position on the RMS values of the ring gear #2 angular accelerations. The sun gear axial position has a minor effect on the RMS value of the ring gear #2 angular accelerations when A_z is larger than 12 mm. The RMS value of the ring gear #2 angular accelerations has a significant increment when A_z= 6 mm. Figure 11(b) shows the effect of the sun gear axial position on the PTP values of the ring gear #2 angular accelerations. The sun gear axial position generally has a minor effect on the PTP value of the ring gear #2 angular accelerations. Overall, the PTP value of the ring gear #2 angular accelerations is relatively small when A_z is <18 mm. Figure 11(c) shows the effect of the sun gear axial position on the RMS values of the ring gear #2 accelerations in x direction. Similar to the results of angular accelerations, the sun gear axial position has a minor effect on the RMS values of the ring gear #2 accelerations in x directions when A_z is larger than 12 mm; and the RMS values of the ring gear #2 accelerations in x directions has a significant increment when A_z= 6 mm. Figure 11(d) shows the effect of the sun gear axial position on the PTP values of the ring gear #2 accelerations in x direction. The sun gear axial position generally has a minor effect on the PTP value of the ring gear #2 accelerations in x direction.

Figure 11.

Effect of the sun gear axial position on ring gear #2 vibrations under operating condition 2. (a) The RMS values of the ring gear angular acceleration, (b) PTP values of the ring gear angular acceleration, (c) RMS values of the ring gear acceleration in x direction, and (d) PTP values of the ring gear acceleration in x direction. PTP: peak-to-peak; RMS: root mean square.

Compare with Figures 8 to 11, it can be found that the vibrations of the ring gear and the sun gear are relatively small when A_z is in the range of 12 to 18 mm. When A_z is in the range of 12 to 18 mm, the RMS values of the ring gear and sun gear vibrations are minimal; and their PTP values are not large. At this time, the vibrations of the double-row PGS are relatively small under both operating conditions. Thus, in practical situations, it is advisable to control the sun gear axial position within this range.

Conclusions

This work establishes a dynamic model of a double-row PGS in the SIMPACK software. The dynamic model considers the mesh forces of the gear pairs and the supporting forces of the bearing. The main conclusions are given as follows:

The RMS and PTP values of the sun gear vibrations in y direction generally decrease with the increment of A_z.

The RMS and PTP values of the ring gear #2 vibrations decrease with the increment of A_z when A_z is <18 mm; and the RMS value increases with the increment of A_z when A_z is larger than 18 mm.

When A_z is in the range of 12 to 18 mm, the RMS values of the ring gear and the sun gear vibrations are minimal; and their PTP values are not large. In this range, the double-row PSG has less vibration, which can significantly improve the reliability and operational stability of the double-row PSG. Thus, in practical situations, it is advisable to control the sun gear axial position within this range.

The assembly associated with the double-row PGS will also have vibrations; and the coupling effect is very complex. However, the study of the coupling mechanism is very important, which can be helpful for vibration control in the system level. Further studies can be conducted in this area.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Yanfang Liu

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Vibration analysis of a double-row planetary gear set considering the sun gear axial position

Abstract

Keywords

Introduction

Problem description

Double-row PGS modeling

Double-row PGS dynamic modeling

Gear meshing force calculation method

Bearing supporting force

Results and discussions

Time-varying mesh stiffness analysis

Time-domain vibrations of the double-row PGS

Effect of the sun gear axial position on its own vibrations

Effect of the sun gear axial position on the ring gear #2 vibrations

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References