Investigation on Mesh and Sideband Vibrations of Helical Planetary Ring Gear Using Structure, Excitation and Deformation Symmetries

Chinese Journal of Mechanical Engineering

Table 7 Exciting conditions for elastic mesh and sideband vibrations

GCDs	Planet counts	Exciting conditions	Wavenumbers	Modulating orders
C = 1	N = 2, 3	l_mZ_r = q_sN or l_sN = q_rZ_r	Q ₁ N	Q ₂ N
	N = 2, 3	l_mZ_r ± 1 = q_sN or l_sN ± 1 = q_rZ_r	Q₁N ± 1	Q₂N ± 1
	N ≥ 4	l_mZ_r = q_sN or l_sN = q_rZ_r	Q ₁ N	Q ₂ N
		l_mZ_r ± 1 = q_sN or l_sN ± 1 = q_rZ_r	Q₁N ± 1	Q₂N ± 1
		Others	Q₁N ± S₁	Q₂N ± S₁
1 < C < N	N = 2, 3	l_mZ_r = q_sN or l_sN = q_rZ_r	Q ₁ N	Q ₂ N
	N ≥ 4	l_mZ_r = q_sN or l_sN = q_rZ_r	Q ₁ N	Q ₂ N
	N ≥ 4	Others	Q₁N ± S₂	Q₂N ± S₂
C = N	–	l_mZ_r = q_sN or l_sN = q_rZ_r	Q ₁ N	Q ₂ N

where S₁ = 2, 3, …, INT(N/2), S₂ = C, 2C, 3C, …, C × INT[N/(2C)], and q_s, q_r, Q₁, and Q₂ are integers