Quarter_Scale_UniCopter

1/4 Scale UniCopter - Power Train

Power Train:
This drawing has been modified.

For an understanding of the drive motor and drive train see; Inrunner+Outrunner_Motor

If the intent is to go with a conventional pitch control for the blade tips then it may be advisable to reduce the diameter of the final crown gear so that the control rods can get by by the gearbox. This will mean that the ratio of the mid-gearbox must be greater.

Miniature bearings: http://www.bocabearings.com/

Motor's rotor drives propeller. Motor's stator drives rotors.

Three pair of spiral bevel gears in one housing?

Ratio, HP, Torque & Losses

At Maximum Vertical Climb:

At Maximum Forward Velocity:

Speed:

Power:

Torque:

Speed:

Power:

Torque:

Ratio:

Loss:

Ratio:

Loss:

[Motor]

12,000

rpm

ft-lb

12,000

rpm

ft-lb

[Prop]

6,000⁽¹⁾

rpm

ft-lb

Intermediate:

12,000

rpm

ft-lb

6,000⁽¹⁾

rpm

ft-lb

Secondary:

2.0

: 1

1.0

2.0

: 1

1.0

X-shaft:

6,000

rpm

156

ft-lb

3,000

rpm

ft-lb

Final:

3.0

: 1

1.0

3.0

: 1

1.0

[Rotor]

2000 ⁽²⁾

rpm

ft-lb

1000

rpm

ft-lb

Total:

6.0

: 1

2.0

6.0

: 1

2.0

The above [Maximum Forward Velocity] columns use an assumed speed distribution between the rotor and the propeller.
(400 fps / (2.5' dia. * (22/7))) * 60 = 3,054 rpm
With rotor radius of 29.25" the tip speed will be 348 mph, 0.47 M

Notes:

Total rotor reduction 8:1

UniCopter Full-scale; Final - Bevel Gears, Ratio 3.375:1, 5 DP, 16/54 teeth. Crown has 10.76" pitch diameter.

UniCopter 1/4-scale (proposed); Final - Bevel Gears, Ratio 4:1 Crown should have 2.7" pitch diameter???

UniCopter Full-scale; Secondary - Bevel Gears, Assembly, 5 DP, 20/30 teeth. Crown has 6" pitch diameter.

UniCopter 1/4-scale (proposed); Secondary - Bevel Gears, Ratio 2:1 Crown should have 1.5" pitch diameter???

The following is a Worm & Wheel workup on its possibility.

It was copied from 1645.html and is to be revised

Hamilton Gear:

This information is Single Enveloping.

- Dimensioning:

FORM: Hamilton Worm Gear Selection. Not yet.

Table F - 7-1

Checked	Symbols:
		Ratio:	8.0:1	7.6 :1	7.5 :1
		Gear teeth & Worm starts :	80 & 10	38 & 5	45 & 6
		Diametral pitch: (nbr. of teeth in wormgear / pitch dia.)	20 DP:	6 DP:	6 DP:
	Ref only	Module pitches: (pitch dia. /nbr. of teeth in wormgear) times 25.4 [for answer in millimeters]	1.270 mm	4.233 mm	4.233 mm
	a	Addendum, inches (nominal) ⁽³⁾	0.144	0.131	0.144
	c	Clearance, inches	0.026	xx	0.026
	C	Center distance, inches ⁽⁵⁾	2.588	3.842	4.686
	d	Nominal pitch diameter of worm, inches	1.345	1.347	1.871
	d_o	Outside diameter of worm, inches	1.633	1.609	2.159
	D	Pitch diameter (std.) of gear in central plane, inches	4.000	6.336	7.500
	D_o	Outside diameter of gear, Normal, inches	5.431	6.732	7.925
	D_oAlso	Outside diameter of gear, Maximum, inches	5.503	6.798	7.997
	D_t	Throat diameter of gear, inches	5.287	6.601	7.781
	F_e	Effective face width of gear, inches	0.879	xx	0.879
	f	Face width of worm, minimum, inches	2.585	xx	2.804
	h_k	Working depth, inches ⁽³⁾	0.288	0.262	0.288
	h_t	Whole depth (ref. addendum + dedendum), inches ⁽³⁾	0.314	0.288	0.314
	L	Lead, inches	2.096	2.620	3.144
	N_G	Number of teeth in gear	30	38	45
	N_W	Number of threads (starts) in worm	10	5	6
	P_n	Normal pitch of worm and gear, inches	0.470"	0.470"	0.470"
	r_G	Gear throat gear radius, inches	0.528	0.543	0.791
	p_X	Axial pitch of worm, inches	0.157	0.157	0.157
	~	Circular pitch of wormgear. ⁽⁴⁾ Same value as axial pitch, inches. Here for definition only.	0.157	0.157	0.157
	λ	Lead angle of worm and helix angle of gear, degrees	26.37º	31.75º	28.13º
	Φ	Normal pressure angle of worm, degrees ⁽³⁾	25º	30º	25º

Hamilton calculation on Boston value on page 81

Hamilton Table F-8-1; except for Boston column.

Hamilton Page K-9; except for Boston column.

This is the distance between 1 wormgear and the worm. The center distance between the 2 wormgears will be slightly less than twice this value.

Table F - 9-1 ~ Worm Dimensions:

Checked	Dimension:	Symbol:	Formula:	6 DP: 4-start	6 DP: 5-start	6 DP: 6-start
	Lead,	L	N_w p_X*	1.570"	2.620"	3.144
	Pitch diameter (nominal) approx.	d	0.45 (C^.875)* \| ⁸√C⁷\|	1.177"	1.347	1.871
	Pitch diameter (nominal)	d	Specified	2.000"	xx	1.871
	Outside Diameter:	d_o	d + 2a	1.633	1.609	2.159
	Minimum Face:	f	4 root((D * a)/ 2)*	2.585"	xx"	2.804"
	Lead angle:	λ	tan^-1 (L /( π d)) ⁽¹⁾*	22.98º	31.75º	28.13º
	Normal Pitch:	p_n	p_X cos(λ)*	0.470"	0.470"	0.470"
	Normal pressure angle:	Φ_n	See table F - 8-1	25º	30º	25º

(1) Trigonometry ~ Inverse tangent function, tan ^-1 or atn

Table F - 9-2 ~ Gear Dimensions:

Checked	Dimension:	Symbol:	Formula:	6 DP: 4-start	6 DP: 5-start	6 DP: 6-start
	Pitch diameter (standard)	D	(N_G p_X ) / π*	4.000"	6.336"	7.500"
	Throat diameter	D_t	2 C - d + 2 * a*	5.287"	6.601"	7.781"
	Outside diameter	D_o	Normal = D_t + a Maximum = D_t +1.5 a*	5.431" 5.503"	6.732" 6.798"	7.925" 7.997"
	Throat Form Radius	r_G	(d - 2 a) /2*	0.51"	0.543"	0.551"
	Effective Face:	F_e	root( (d + h_k )² - d²)	0.879"	0.880"	0.879"

- Efficiency:

Rubbing velocity of the worm (feet per minute) = (π * pitch dia. of worm * Rpm or worm) / (12 * cosine of Lead Angle) = (3.14 * d * 4500) / (12 * cos(λ))

For 6 DP, 4-starts = (3.14 * 1.345 * 4500) / (12 * 0.896) = 1,768 fpm

For 6 DP, 5-starts = (3.14 * 1.347 * 4500) / (12 * 0.850) = 1,866 fpm

For 6 DP, 6-starts = (3.14 * 1.871 * 4500) / (12 * 0.882) = 2,498 fpm

________________________

Efficiency of Worm and Gear Sets in Percent: From Table F - 10-1

For 6 DP, 4-starts: factor η = 95.25.

For 6 DP, 6-starts: factor η = 96.0

For 6 DP, 6-starts: factor η = 96.0

- Horsepower Ratings: Note that the calculations below are based on the optimal materials etc and they do not take into account the extra activity on the worm due to its driving of 2 wormgears.

Durability Horsepower Rating:

Checked	Worm:		P_ac = (n_w s_ac * C_v * Z * p * D^1.8) / (1980 * η * m_G) =*
		6 DP: 4-start	(4,500 * 8,800 * .065 * 1.230 * 0.524 * 18.119) / (1980 * 95.25 * 7.5) = 21 HP
		6 DP: 5-start	(4,500 * 8,800 * .065 * 1.245 * 0.524 * 27.750) / (1980 * 96 * 7.6) = 32 HP
		6 DP: 6-start	(4,500 * 8,800 * .064 * 1.677 * 0.524 * 37.593) / (1980 * 96 * 7.5) = 59 HP
	Gear:		P_ac = (n_w s_ac * C_v * Z * p * D^1.8) / (1980 * η * m_G) =*
		6 DP: 4-start	(4,500 * 2,200 * .133 * 1.235 * 0.524 * 18.119) / (1980 * 95.25 * 7.5) = 10.9 HP
		6 DP: 5-start	(4,500 * 2,200 * .127 * 1.240 * 0.524 * 19.913) / (1980 * 96 * 7.6) = 11 HP
		6 DP: 6-start

Strength Horsepower Rating:

Checked	Worm:		P_at = (n_w s_at * K_v * p * F * R_r * D * Cos(λ)* / (1100 * η * m_G) =
		6 DP: 4-start	(4,500 * 50,000 * 0.15 * 0.524 * 0.879 * 1.066 * 5.000 * 0.896 / 1100 * 95.25 * 7.5 = 94 HP
		6 DP: 5-start	(4,500 * 50,000 * 0.15 * 0.524 * 0.880 * 1.069 * 6.336 * 0.850 / 1100 * 96 * 7.6 = 111 HP
		6 DP: 6-start
	Gear:		P_at = (n_w s_at * K_v * p * F * R_r * D * Cos(λ)* / (1100 * η * m_G) =
		6 DP: 4-start	(4,500 * 10,000 * 0.29 * 0.524 * 0.879 * 1.066 * 5.000 * 0.896 / 1100 * 95.25 * 7.5 = 36 HP
		6 DP: 5-start	(4,500 * 10,000 * 0.29 * 0.524 * 0.880 * 1.066 * 6.336 * 0.850 / 1100 * 96 * 7.6 = 43 HP
		6 DP: 6-start

- Weight:

The following weights are rough approximations, for now.

Carbon Steel; 0.2835 lb per sq-in.

Bronze: 0.3171 lb per sq-ft.

Checked	Hamilton Gear Specs:	Worm:	Wormgear: ⁽¹⁾	Set of 3 gears:
	6 DP: 4-start ~ 30 & 4	1.6" dia * 5.5" = 11.1"³ = 3.1 lbs	5.5" dia * 0.9" = 21.4"³ = 6.9 lbs	17 lbs ⁽¹⁾
	6 DP: 5-start ~ 38 & 6	1.6" dia * 6.8" = 13.7"³ = 3.9 lbs	6.8" dia * 0.9" = 32.7"³ = 10.5lbs	25 lbs ⁽¹⁾
	6 DP: 6-start ~ 45 & 6	2.2" dia * 8.0" = 30.4"³ = 8.6 lbs	8.0" dia * 0.9" = 45.3"³ = 14.5 lbs	38 lbs ⁽¹⁾

(1) Note that the wormgears can have quit a bit of meat cut off them.

Last Revised: June 7, 2008