Calculation of Cylindrical Involute Gears

CYLINDRICAL INVOLUTE GEARS
CALCULATION REPORT
Order	Dware
Project	Mixer
Sub project	Gear Box
Item	Stage 4 m4
ID Gear1	z14
ID Gear2	z61
Calculated by	André Dewisspelaere
Company	Dware
Date	09/06/2023

1	1. Standard basic rack	Symbol	Unit	Gear1	Gear2
2	Pressure angle	α_P	°.dec	20.000	20.000
3	Addendum coefficient	k_haP	--	1.000	1.000
4	Dedendum coefficient	k_hfP	--	1.250	1.250
5	Root fillet radius coefficient	k_ρfP	--	0.300	0.300
6	Reference to standard	--	--	DIN 867	DIN 867
7	2. Calculation basic rack	Symbol	Unit	Gear1	Gear2
8	Normal module	m_n	mm	4.000	4.000
9	Addendum	h_aP	mm	4.000	4.000
10	Dedendum	h_fP	mm	5.000	5.000
11	Tooth depth	h_P	mm	9.000	9.000
12	Bottom clearance	c_P	mm	1.000	1.000
13	Root fillet radius	ρ_fP	mm	1.200	1.200
14	Pitch	p_P	mm	12.566	12.566
15	Tooth thickness	s_P	mm	6.283	6.283
16	Space width	e_P	mm	6.283	6.283
17	Tooth thickness at tip	s_aP	mm	3.371	3.371
18	Space width at tip	e_aP	mm	9.195	9.195
19	Tooth thickness at root	s_fP	mm	9.923	9.923
20	Space width at root	e_fP	mm	2.643	2.643

1	3. Geometry calculation	Symbol	Unit	Gear1	Gear2
2	Normal module	m_n	mm	4.00000	4.00000
3	Normal diametral pitch	P_dn	/in	6.35000	6.35000
4	Number of teeth	z	--	21	66
5	Face width	b	mm	60.00	60.00
6	Reference helix angle	β	°.dec	14.00000	14.00000
7	Helix direction	--	--	right	left
8	Profile shift coefficient	x	--	0.4940	0.4870
9	Center distance	a	mm	183.000	183.000
10	Gear ratio	u	--	3.1429	3.1429
11	Transverse module	m_t	mm	4.1224	4.1224
12	Reference diameter	d	mm	86.572	272.082
13	Operating pitch diameter	d_w	mm	88.345	277.655
14	Base diameter	d_b	mm	81.057	254.749
15	Addendum truncation coefficient	k	--	-0.063	-0.063
16	Tip diameter	d_a	mm	98.022	283.476
17	Theoretical root diameter	d_f	mm	80.524	265.978
18	Addendum	h_a	mm	5.725	5.697
19	Dedendum	h_f	mm	3.024	3.052
20	Tooth depth	h	mm	8.749	8.749
21	Bottom clearance	c	mm	1.000	1.000
22	Transverse pressure angle	α_t	°.dec	20.56171	20.56171
23	Transv operating pressure angle	α_wt	°.dec	23.43655	23.43655
24	Normal tooth thickness	s_n	mm	7.722	7.701
25	Normal crest width	s_an	mm	2.391	3.126
26	Normal tooth thickness at base cir	s_bn	mm	8.538	11.266
27	Normal tooth thickness at V-circle	s_vn	mm	6.339	6.298
28	Normal space width	e_n	mm	4.845	4.865
29	Normal space width at tip circle	e_an	mm	11.722	9.933
30	Normal space width at base circle	e_bn	mm	3.270	0.542
31	Normal space width at V-circle	e_vn	mm	6.765	6.437
32	Transverse contact ratio	ε_α	--	1.397	1.397
33	Overlap ratio	ε_β	--	1.155	1.155
34	Total contact ratio	ε_γ	--	2.552	2.552
35	Ratio axial/tangential force	F_a/F_t	--	0.249	0.249
36	Gear bounds respected	--	--	yes	yes
37	Face width/module ratio	b/mn	--	15.00	15.00
38	Face width/reference diam ratio	b/d	--	0.69	0.22
39	Face width/center distance ratio	b/a	--	0.33	0.33
40	High surface and bend strength P7	PCl	--	P7	P7
41	Sum profile shift coefficients	Sx,Sx/2	--	0.981	0.490
42	Directive sum number of teeth	Sumz'	--	88	88
43	Sum number of teeth	Sumz	--	87	87
44	Normal pitch	p_n	mm	12.566	12.566
45	Transverse pitch	p_t	mm	12.951	12.951
46	Transverse base pitch	p_bt	mm	12.126	12.126
47	Intersection circle diameter	d_apt	mm	105.37	302.08
48	Profile shift factor intersection	x_G1pt	--	1.35	2.75
49	Space root intersection circle	d_fpt	mm	--	--
50	Profile shift fact root intersectn	x_G5pt	--	--	--
51	Profile shift circle diameter	d_v	mm	90.524	275.978
52	Virtual number of teeth	z_n	--	22.8	71.7
53	Sum virtual number of teeth	Szn,Szn/2	--	94.6	47.3