CYLINDRICAL INVOLUTE GEARS
CALCULATION REPORT
Order	Niemann-Winter
Project	Planetary Gear Train
Sub project	Calculation Example
Item	Band II Edition 2 page 364
ID Gear1	z1=17
ID Gear2	z2=49
Calculated by	André Dewispelaere
Company	Dware - Belgium
Date	09/06/2023

1	1. Plan gear train verification ca	Symbol	Unit	Data
2	Planetary gear type	--	--	idler
3	2. Motion state	Symbol	Unit	Rot speed	State
4	Rotation speed sun gear	n1	rpm	100.000	imposed
5	Rotation speed ring gear	n4	rpm	0.000	imposed
6	Rotation speed planet carrier	nc	rpm	12.800	dependent
7	Transmission is speed	--	--	reducing
8	Modulus	mn	mm	5.500
9	Face width	b	mm	73.4
10	Helix angle	β	°.dec	0.00000
11	Number of planets	p	--	3
12	Desired fixed carrier ratio	i14	--	-6.8000
13	3. Input pair1: sun-planet gear	Symbol	Unit	Sun gear1	Planet gr2
14	Number of teeth	z1,2	--	17	49
15	Center distance	a12	mm	183.000
16	Sum profile shift coefficients	(x1 + x2)	--	0.0000
17	Profile shift coefficient	x1,2	--	0.2570	0.0000
18	4. Input pair2: planet-ring gear	Symbol	Unit	Planet gr3	Ring gear4
19	Number of teeth	z3,4	--	49	-115
20	Profile shift coefficient	x3	--	0.0240	--
21	5. Calcul pair1: sun-planet gear	Symbol	Unit	Sun gear1	Planet gr2
22	Center distance	a12	mm	183.000
23	Sum profile shift coefficients	(x1 + x2)	--	0.2810
24	Good balanced gearing P4	P-Cl	--	P4
25	Profile shift coefficient	x1,2	--	0.2570	0.0240
26	Reference diameter	d1,2	mm	93.500	269.500
27	Tip diameter	da1,2	mm	107.327	280.764
28	6. Calcul pair2: planet-ring gear	Symbol	Unit	Planet gr3	Ring gear4
29	Center distance	a34	mm	-183.000
30	Sum profile shift coefficients	(x3 + x4)	--	-0.2810
31	Profile shift coefficient	x3,4	--	0.0240	-0.3050
32	Reference diameter	d3,4	mm	269.500	-632.500
33	Tip diameter	da3,4	mm	280.764	-624.855
34	7. Conditions	Symbol	Unit	Data
35	Planets insert condition satisfied	--	--	yes
36	Condition (x3 + x4) <= 0 satisfied	--	--	yes
37	Condition x4 <= 0 satisfied	--	--	yes
38	Face width/reference diamet ratio	b/d1	--	0.79
39	8. Transmission ratio	Symbol	Unit	Data
40	Fixed carrier transm ratio	i14	--	-6.7647
41	Transm ratio sun gear-planet carr	i1c	--	7.7647
42	Transm ratio sun gear-planet gear	i12	--	2.8824
43	Transm ratio planet gear-ring gear	i34	--	-2.3469
44	9. Rotation speeds	Symbol	Unit	Data
45	Rotation speed sun gear shaft	n1	rpm	100.000
46	Rotation speed ring gear shaft	n4	rpm	0.000
47	Rotation speed planet carr shaft	nc	rpm	12.879
48	10. Relative rotation speeds	Symbol	Unit	Data
49	Relative rotation speed sun gear	n1r	rpm	87.121
50	Relative rotation speed planet gr	n2r	rpm	-30.226
51	Relative rotation speed ring gear	n4r	rpm	-12.879
52	11. Torques	Symbol	Unit	Data
53	Torque on sun gear shaft	T1	Nm	6875.492
54	Torque on ring gear shaft	T4	Nm	46510.641
55	Torque on planet carrier shaft	Tc	Nm	-53386.133
56	12. Forces	Symbol	Unit	Data
57	Transverse tangent force sun gr 1	Ft1	N	-49023.12
58	Transverse tangent force plan gr 2	Ft2	N	49023.12
59	Transverse tangent force plan gr 3	Ft3	N	49023.12
60	Transverse tangent force ring gear	Ft4	N	-49023.12
61	Transv force planet bearing pivot	Fc	N	98046.24