UNIVERSITATEA TRANSILVANIA DIN BRA+OV
Catedra Design de Produs "i Robotic/
Simpozionul na@ional cu participare interna@ionalA
PRoiectarea ASIstatA de Calculator
P R A S I C ' 02
Vol. II - Organe de ma"ini. Transmisii mecanice
7-8 Noiembrie
Bra ov, România
ISBN 973-635-075-4
THE MECHANICAL ADVANTAGE OF MANUAL WORM GEARBOXES
USED TO DRIVE “QUARTER-TURN” VALVES
Gheorghe MILOIU*, Drago" MILOIU**
*S.C. CONFIND Câmpina
**Universitatea POLITEHNICA Bucure ti (student)
Abstract: The mechanical advantage is a basic parameter of worm gearboxes used to drive valves: ratio of
effective multiplication of the torque, from the hand wheel to valve stem. This paper describes the calculus
algorithm for the mechanical advantage of worm gear actuators for “quarter-turn” valves. The evaluation of
the mechanical advantage is possible even from the designing stage. The paper presents some numerical
results which show the influence of their constructive parameters and the tribological conditions from the
links of these actuators.
Keywords: mechanical advantage, “quarter-turn” worm gearboxes, worm gearboxes, valve actuator.
1. Introduction
“Quarter-Turn” valves, such as butterfly valves,
ball valves, can be driven by manual, electrical,
pneumatic or hydraulic actuators. Double driving
systems, especially pneumatic-manual ones, are also
used. In principle, a mechanical “quarter-turn”
actuator is either a worm gearbox (to which, for
higher output torques, one or two additional
cylindrical steps are attached), or a planetary
gearbox with one control gear wheel or with two
central gear wheels (in more steps), or a lever
actuator.
This paper deals with the most widely used type
of “quarter-turn” actuators: the worm gearbox.
These actuators are used for driving torques ranging
between 0.1-300 kN*m, and they generally
manufactured like this: with manual input drive for
torques up to 100 kN*m and with electrical input
drive in the interval 1-300 kN*m.
The basic parameters of worm gearboxes for
“quarter-turn” valves are the following:
- valve stem driving torque, M2 ;
- driving torque M1 ;
- transmission ratio, u ;
- efficiency, ;;
- valve flange, as per ISO 5211.
Usually, the companies producing actuators do
not speak about the efficiency ;, but about a
synthetic feature: mechanical advantage, defined as
a ratio of effective multiplication of the torque:
kMAw= M2 / M1. Obviously, kMA can be also
expressed as kMA = ;* u.
Fig. 1. Mastergear worm gearbox
272
Fig. 2. Tarp RAF worm gearbox
By our knowledge, this paper is the first one
published on the topic “the mechanical advantage of
valve actuators”.
This paper enables the evaluation of the
mechanical advantage of worm gear actuators for
“quarter-turn” valves, even from the designing stage,
and the review of the influence of their constructive
parameters and the tribological conditions from the
links of these actuators.
2. The construction of a representative
actuator
means of the adapter 9. Driving is done with a hand
wheel.
The valve position is indicated by the arrow
from the upper cap 12.
At the companies quoted in [2], the worm gear
actuators have specific designs as regards the worm
and its bearing system, the worm wheel supporting
system, the housing design.
3. Establishing the mechanical advantage by
calculus
Since
The “quarter-turn” actuators with worm gear
will be described based on the design developed by
the company MASTER GEAR [2], shown in Figure
1, specially developed for the light series of drives:
housings made of pressure-cast aluminum, manual
drive, torques up to 800 N*m.
The MG actuator features the following basic
elements: a body composed of the case 1 (to the
fixed onto the valve) and the case 2 (completing the
body), a worm 3 fitted onto the shaft 4 by means of a
traverse pin 5, a specially shaped worm wheel
(quadrant) 6, the sleeves 7 and the axial bearings 8
supporting the worm, the adapter 9 mounted along
splines within the quadrant, two pins 10 and two
self-locking nuts 11 – adjustable limit stops.
The actuators is fixed onto the valve by means of
the housing 1 and is coupled to the valve stem by
k MA = M 2 / M 1 = u,
to calculate the mechanical advantage means to
establish the torque M2 for a given value of M1,
respectively to evaluate the efficiency ;. There is
also another equivalent way, more practical: to
admit the worm torque in the meshing area (Ma) and
evaluate the necessary torque (M1) at the hand wheel
and the torque (M2) obtained at the driving bush.
The diagram of the worm line torque is
shown in Figure 3, and in Figure 4 – the torque
diagram for the worm wheel line.
Symbols used:
m – axial module of the worm,
a – center distance,
z1 – number of leads of the worm,
273
Fig. 3. The torque on the worm line
q – the diameter coefficient of the worm,
dm1 = m*q – the pitch diameter of the worm,
&m = arctg( z 1 / q ) – the angle of the medium
helix of the worm,
l1, l2, d1, d2 – dimensions, mm, Figure 3,
d3, d4, d6, d7, b2, b3, b4 – dimensions, mm,
Figure 4,
fAN and -AN – the friction coefficient and angle
between the teeth of the worm
and those of the worm wheel,
f1R – the coefficient for the friction in the radial
bearings of the input shaft,
f1A – the friction coefficient of the axial bearing
of the input shaft,
f2R – the coefficient for friction in the radial
bearings of the worm wheel,
f2A – the coefficient for friction in the axial
bearing of the worm wheel,
M – torque, in N*m.
Fig.4.The torque on the worm wheel line
for
AN
= arctg ( f AN / cos
n
),
n
= 20 o.
The friction torque on the worm line – MAN –
the friction torque in the meshing area, M12R – the
friction torque in the bearing of the worm, are given
by the expressions:
M AN = M a 1
tg
tg (
m
m
+
AN
)
;
M 1R = 0.00025d1 f1R
[Fa1d m1 /(l1 + l 2 ) + Fr1 ]2 + Ft12
+
[Fr1
+
Fa1d m1 /(l1 + l 2 )]2 + Ft12 ;
M 1 A = 0.00025(d1 + d 2 ) f1A FA1 .
Admitting Ma – the torque at the worm in the
meshing area, the expressions of the gear forces
(components of the normal force) may be written:
The input shaft (worm) driving torque M1
should be:
Ft1 = 2000M a / d m1;
M 1 = M a + M 1R + M 1 A .
Ft 2 = Ft1 / tg (
m
+
AN
Fr1 = (Ft 2 cos
AN tg
n
);
) / cos(
m
Fa1 = Ft 2 ; Fa 2 = Ft1 ; Fr 2 = Fr1 ;
+
AN
);
The torques of friction on the line of the worm
wheel is: M2R – the friction torque in the radial
bearings of the quadrant and the adapter bush; M2A
– the friction torque in the axial bearing of the
quadrant, respectively:
274
M 2 R = 0 . 00025 f 2 R
d3
+ d4
Fa 2 d m 2 + Fr 2 (b2 + b3 )
2b2 + b3 + b4
2
+
Fr 2 (b2 + b4 ) Fa 2 d m 2
2 b 2 + b3 + b 4
Ft22
+
4
2
+
Ft 22
4
M 2 A = 0.00025(d 3 + d 4 ) f 2 A Fa 2 .
The torque M2 available at the adapter bush (at
the valve stem) is
M 2 = (M a
M AN ) z 2 / z1
M 2R
M 2A.
Knowing the torques M1 and M2, the mechanical
advantage of the gearbox may be calculated
k MA = M 2 / M 1
and also the gearbox efficiency
= k MA z1 / z 2 .
4. The torques by gearbox elements
Based on the algorithm presented, numerical
research has been done, partially shown in Figure 5,
6 and 7, for a gearbox with a=40, m=1.5, and
various q and z2: q / z2 = 10 / 44; 12.5 / 40; 15 / 38;
17.5 / 36; 20 / 34.
The constructive elements of interest, shown in
Figure 3 and 4, are: a = 40, l1 = 42, l2 = 13, d1 = 12,
Fig. 5. The torques on the worm and worm
wheel lines(a=40)
d2 =20, d3 = 43.5, d4 = 38.1, d6 = 42.3, d7 = 52, b2 = 2,
b3 = 16, b4 = 10.
The torque available at the worm in the meshing
area was then admitted, Ma = 10 N*m.
An example of torque distribution along the
lines of the worm and the worm wheel is given in
Figure 5.
The condition is specified on the figure. It is
found that some 50% of Ma is consumed in the
friction between the gear teeth (5.19 N*m), and the
friction torques in the bearings of the input
Fig. 6. The influence of the diametral coefficient of the worm on the mechanical advantage kMA
and the efficiency ; for the gearbos with a = 40
fAN = 0.06 … 0.10 ; f1R = 0.08 ; f1A = 0.08 ; f2R = 0.08 ; f2A = 0.08
275
shaft are M1R = 1.38 N*m and M1A = 4.11. The
necessary torque for driving the worm is M1 = 15.49
N*m.
The torque at the worm wheel, resulted from
meshing, is 192.45 N*m. Out of this torque, the
friction from the quadrant bearings consumes M2R =
5.98 N*m and M2A = 184.7 N*m.
The greatest frictions are found in the meshing
area in the axial bearing of the input shaft. The
frictions in the quadrant bearing are small.
5. The influence of gear parameters on the
mechanical advantage and the efficiency.
Some results are shown in fig. 6: at left – the
mechanical advantage kMA, at right – the efficiency
;. The negative influence of the worm diameter
increase, respectively the diameter coefficient q, can
be noticed. For example, when fAN = 0.08, the
mechanical advantage is kMA = 14.10 at q = 10, to
decrease to kMA = 8.26 at q = 20, and the efficiency
decreases from ; = 32.04% to 24.29%.
Fig. 7. The influence of tribological conditions on the mechanical advantage kMA
for the gearbox with a = 40
b
fAN
0.06 0.12
0.08
c
0.08
Figure
a
f1R
0.08
f1A
0.02
f2R
0.08
f2A
0.08
Figure
d
fAN
0.06
f1R
0.06
f1A
0.02
0.040.10
0.08
0.02
0.08
0.08
e
0.08
0.08
0.02
0.02 0.1
0.08
0.08
f
0.06 –
0.12
0.08
0.02
- 0.1
f2R
0.04
– 0.1
0.08
0.08
f2A
0.08
0.04
– 0.1
0.08
276
The influence of the gear parameters (q, z2) for
three gearboxes of the coefficient for the friction
between the teeth: fAN = 0.06, 0.08, 0.10, is shown
in Figure 6.
6. The influence of tribologic conditions on
the mechanical advantage
The parameters characterizing the tribologic
conditions in “quarter-turn” worm gearboxes are:
the coefficient for friction between the teeth in mesh
– fAN, the coefficients for friction in the input shaft
bearings – f1R and f1A, the coefficients for friction in
the worm wheel bearings – f2R and f2A. The
influence of these parameters is shown in Figure 7.
The variation of the parameter fAN significantly
influences the mechanical advantage kMA (Figure 7,
a). For example, at q = 15, kMA = 14.74 at fAN = 0.06
and kMA = 10.45 at fAN = 0.12, respectively when the
friction between the teeth of the worm and those of
the wheel are double, kMA decreases by about 30%.
The variation within large limits of the
coefficient for friction in the radial bearings of the
input shaft (from f1R = 0.04 to 0.10) has a significant
influence on the parameter kMA: about 10% (Figure
7b).
In turn, the modification in the friction
conditions from the axial bearings of the input shaft
has an important influence (Fig. 7, c). For instance,
when q = 12.5, at f1A = 0.08, kMA = 14.89, and when
f1A = 0.10, kMA = 11.19, respectively kMA decreases
by some 25%.
One could see in Figure 7, d and 7, e that
modifying the friction conditions from the wheel
bearings, f2R and f2A has insignificant influence on
the parameter kMA: kMA = 15.45…15.05 (some 2%),
at f2R = 0.04…0.08 – for q = 15 and kMA =
13.04…12.95 (about 0.7%), at f2A = 0.04…0.10 –
again for q = 15.
With this remark, the influence of the
tribological parameters fAN and f1A for the gearbox
having the geometrical parameters q = 12.5 and z =
40 is reviewed in Figure 7, e.
In the extreme cases, the following values are
found for the parameter kMA: 16.73 for fAN = 0.06
and f1A = 0.02 and 9.58 for fAN = 0.12 and f1A = 0.10.
The conditions of friction – lubrication between the
gear teeth and from the axial bearings of the input
shaft have strong influence (1.75 / 1) on the
mechanical advantage.
7. Conclusions for the design of “quarterturn” gearboxes
Even if certain values for the mechanical
advantage can not be offered, since the five friction
coefficients fAN, f1R, f1A, f2R, f2A are difficult to be
evaluated, the model described offers the possibility
to handle the constructive design of “quarter-turn”
worm gearboxes in view of increasing the
mechanical advantage.
1. Using worms with as small a diametral
coefficient as possible is an advantage (observing
the strength conditions) so is the use of axial
bearings with the lowest friction (this is why many
gearbox designs have the input shaft supported onto
axial bearings).
2. As good lubrication as possible should be
ensured for both the teeth of the worm and of the
worm wheel.
Bibliography
1. Miloiu, G., Constantin, T., VintilA, H.
Multicriterial selection of parameters for
cylindrical worm gears. In: Simpozionul
PRASIC’98, Universitatea din Bra ov, 1998,
Vol. 2 – Organe de ma ini. Transmisii
mecanice, p.289 - 294.
2. Catalogues of several companies specialized in
manufacturing valve actuators: Mastergear,
Torkmatic – England; Limitorque, Dyna –
toque, Keystone, Kenneth Elliott, Bray Valve &
Controls, Diamond – USA; Biffi, Sirca – Italy;
KSB – Amri, Sapag – France; Confind, Neptun,
Robinete Raf – Romania; Alecto, Matinex –
Netherlands.