Permissible stresses for bending fatigue strength

This calculation excludes fatigue rapture of teeth. The permissible stresses are calculated separately for pinion and wheel as per the following formula:

RAPTURE:

, МПа where  – average hardness value –safety ratio

2. Designedcalculationofhelicalgear

Purpose of calculation:assessment of interaxial spacing and other parameters of gear, excluding chipping of teeth surface of operating gear.

Estimate value of interaxial spacing

, мм

where  – torque at the wheel, Н m;

–ratio for uneven load spread along contact line  – ratio of relative wheel width for any wheels under symmetrical position in relation to supports.

Calculated value (мм) should be rounded to nearest big figure according to GOST 2185-66.

1st row	40	50	63	80	100	125	160	200	315	400	500	630
2nd row	–	–	71	90	112	140	180	224	280	355	450	560

Note: values of the 1^st row are preferable.

Further calculation is recommended to be done in the following sequence:

Gearing module is to be set as , mm, with rounding up to nearest standard value.

Standard row (selection) of modules

	1st row	1	1,25	1,5	2	2,5	3	4	5	6
	2nd row			1,75	2,25	2,75	3,5	4,5	5,5	7

In order to set linear dimensions – diameters, lengths, heights etc the standards define rows as specified in Table 6.

Table 6.

Normal linear dimensions (GOST 6636-69)

Ra 20	Ra 40	Ra 20	Ra 40	Ra 20	Ra 40	Ra 20	Ra 40
1,0	1,00	5,6	5,6	32	32	180	180
	1,05		6,0	34	34		190
1,1	1,10	6,3	6,3	36	36	200	200
	1,15		6,7		38		210
1,2	1,20	7,1	7,1	40	40	220	220
	1,30		7,5		42		240
1,4	1,40	8,0	8,0	45	45	250	250
	1,50		8,5		48		260
1,6	1,60	9,0	9,0	50	50	280	280
	1,70		9,5		53		300
1,8	1,80	10,0	10,0	56	56	320	320
	1,90		10,5		60		340
2,0	2,00	11,0	11,0	63	63	360	360
	2,10		11,5		67		380
2,2	2,20	12,0	12,0	71	71	400	400
	2,40		13,0		75		420
2,5	2,50	14,0	14,0	80	80	450	450
	2,60		15,0		85		580
2,8	2,80	16,0	16,0	90	90	500	500
	3,00		17,0		95		530
3,2	3,20	18,0	18,0	100	100	560	560
	3,40		19,0		105		600
3,6	3,60	20,0	20,0	110	110	630	630
	3,80		21,0		120		670
4,0	4,00	22,0	22,0	125	125	710	710
	4,20		24,0		130		750
4,5	4,50	25,0	25,0	140	140	800	800
	4,80		26,0		150		850
5,0	5,00	28,0	28,0	160	160	900	900
	5,30		30,0		170		950

Note. From rows (Ra5, Ra10, Ra20, Ra40) as set by the standards the rows Ra20, Ra40 are also indicated with smaller gradation

All catching parameters are expressed via the following module

Width of the wheel is defined by the following equation:

, мм.

Width of the pinion is set as , мм.

Calculated dimensions should be verified with standard ones as per GOST 6636-69 (Table 6).

Helix angle to be set as follows: .

Minimum helix angle is to be .

Then the following parameters shall be defined:

• total number of gear teeth , taking as whole part of integer ;

• number of pinion teeth , rounding up to whole integer ;

• number of wheel teeth .

Helix angle value is to be refined .

Actual gear ratio shall be refined and its deviation from the set value:

, .

Then calculation of geometrical parameters of toothed wheels is to be done according to formulas as specified in Table 7

Table7

Calculation of geometrical parameters of toothed wheels

Parameter		Symbol	Formula
1		2	3
1. Reference diameter, mm	pinion
	wheel

Extension of Table.

1		2	3
2. Interaxial spacing, mm
3. Tip diameter mm	pinion
	wheel
4. Gash diameter, mm	pinion
	wheel