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Functions for Self-Locking Gears | Gear Options Journal Your Useful resource to the Gear Business

Functions for Self-Locking Gears | Gear Options Journal Your Useful resource to the Gear Business

2023-01-27 20:16:05

In most gear drives, when driving torque is all of a sudden decreased on account of energy off, torsional vibration, energy outage, or any mechanical failure on the transmission enter facet, then gears can be rotating both in the identical path pushed by the system inertia, or in the other way pushed by the resistant output load because of gravity, spring load, and so forth. The latter situation is called backdriving. Throughout inertial movement or backdriving, the pushed output shaft (load) turns into the driving one and the driving enter shaft (load) turns into the pushed one. There are numerous gear drive functions the place output shaft driving is undesirable. To be able to forestall it, several types of brake or clutch gadgets are used.

Nevertheless, there are additionally options within the gear transmission that forestall inertial movement or backdriving utilizing self-locking gears with none further gadgets. The most typical one is a worm gear with a low lead angle. In self-locking worm gears, torque utilized from the load facet (worm gear) is blocked, i.e. can not drive the worm. Nevertheless, their utility comes with some limitations: the crossed axis shafts’ association, comparatively excessive gear ratio, low pace, low gear mesh effectivity, elevated warmth era, and so forth.

Fig. 1: Typical (left) and self-locking (proper) gears; 1 – driving pinion, 2 – pushed gear; blue coloration reveals the conventional driving operation, purple coloration – the case when the pushed gear turns into the driving by output load.

Additionally, there are parallel axis self-locking gears [1, 2]. These gears, in contrast to the worm gears, can make the most of any gear ratio from 1:1 and better. They’ve the driving mode and self-locking mode, when the inertial or backdriving torque is utilized to the output gear. Initially these gears had very low (<50 p.c) driving effectivity that restricted their utility. Then it was proved [3] that top driving effectivity of such gears is feasible. Standards of the self-locking was analyzed on this article [4]. This paper explains the precept of the self-locking course of for the parallel axis gears with symmetric and uneven enamel profile, and reveals their suitability for various functions.

Desk 1

Self-Locking Situation

Determine 1 presents standard gears (a) and self-locking gears (b), in case of backdriving. Determine 2 presents standard gears (a) and self-locking gears (b), in case of inertial driving. Virtually all standard gear drives have the pitch level P positioned within the energetic portion the contact line B1-B2 (Determine 1a and Determine 2a). This pitch level location gives low particular sliding velocities and friction, and, because of this, excessive driving effectivity. In case when such gears are pushed by output load or inertia, they’re rotating freely, as a result of the friction second (or torque) shouldn’t be ample to cease rotation. In Determine 1 and Determine 2:

1– Driving pinion
2 – Pushed gear
db1, db2 – base diameters
dp1, dp2 – pitch diameters
da1, da2 – outer diameters
T1 – driving pinion torque
T2 – pushed gear torque
T’2 – driving torque, utilized to the gear
T’1 – pushed torque, utilized to the pinion
F – driving drive
F’ – driving drive, when the backdriving or inertial torque utilized to the gear
aw – working transverse stress angle
g – arctan(f) – friction angle
f – common friction coefficient

Fig. 2: Typical (prime) and self-locking (backside) gears; 1 – driving pinion, 2 – pushed gear; blue coloration reveals the conventional driving operation, purple coloration – the case when the pushed gear turns into the driving by inertia.

To be able to make gears self-locking, the pitch level P must be positioned off the energetic portion the contact line B1-B2. There are two choices. Choice 1: when the purpose P is positioned between a middle of the pinion O1 and the purpose B2, the place the outer diameter of the gear intersects the contact line. This makes the self-locking doable, however the driving effectivity can be low underneath 50 p.c [3]. Choice 2 (figs 1b and 2b): when the purpose P is positioned between the purpose B1, the place the outer diameter of the pinion intersects the road contact and a middle of the gear O2. One of these gears will be self–locking with comparatively excessive driving effectivity > 50 p.c.

One other situation of self-locking is to have a ample friction angle g to deflect the drive F’ past the middle of the pinion O1. It creates the resisting self-locking second (torque) T’1 = F’ x L’1, the place L’1 is a lever of the drive F’1. This situation will be introduced as L’1min > 0 or
(1) Equation 1
(2) Equation 2

the place:
u = n2/n1 – gear ratio,
n1 and n2 – pinion and kit variety of enamel,
– involute profile angle on the tip of the gear tooth.

Design of Self-Locking Gears

Self-locking gears are customized. They can’t be fabricated with the requirements tooling with, for instance, the 20o stress and rack. This makes them very appropriate for Direct Gear Design® [5, 6] that gives required gear efficiency and after that defines tooling parameters.

Fig 3: Direct Gear Design tooth profile definition; proper – symmetric tooth; left – uneven tooth; da – tooth tip circle diameter; db – base circle diameter; n– involute intersection profile angle; subscripts “d” and “c” are for the drive and coast flanks of the uneven tooth.

Direct Gear Design presents the symmetric gear tooth shaped by two involutes of 1 base circle (Determine 3a). The uneven gear tooth is shaped by two involutes of two totally different base circles (Determine 3b). The tooth tip circle da permits avoiding the pointed tooth tip. The equally spaced enamel kind the gear. The fillet profile between enamel is designed independently to keep away from interference and supply minimal bending stress. The working stress angle aw and the contact ratio ea are outlined by the next formulae:

– for gears with symmetric enamel

(3) Equation 3

(4) Equation 4

– for gears with uneven enamel

(5) Equation 5

(6) Equation 6

(7) Equation 7

See Also

the place:
inv(x) = tan x – x – involute operate of the profile angle x (in radians).
Circumstances (1) and (2) present that self-locking requires excessive stress and excessive sliding friction within the tooth contact. If the sliding friction coefficient f = 0.1 – 0.3, it requires the transverse working stress angle to aw = 75 – 85o. In consequence, the transverse contact ratio ea < 1.0 (sometimes 0.4 – 0.6). Lack of the transverse contact ratio must be compensated by the axial (or face) contact ratio eb to ensure the entire contact ratio eg = ea + eb ≥ 1.0. This may be achieved through the use of helical gears (Determine 4). Nevertheless, helical gears apply the axial (thrust) drive on the gear bearings. The double helical (or “herringbone”) gears (Determine 4) enable to compensate this drive.

Fig 4: Self-locking gear design; a – helical gears; b – double helical gears.

Excessive transverse stress angles lead to elevated bearing radial load that might be as much as 4 to 5 occasions greater than for the standard 20o stress angle gears. Bearing choice and gearbox housing design must be performed accordingly to carry this elevated load with out extreme deflection.

Software of the uneven enamel for unidirectional drives permits for improved efficiency. For the self-locking gears which can be used to forestall backdriving, the identical tooth flank is used for each driving and locking modes. On this case uneven tooth profiles present a lot greater transverse contact ratio on the given stress angle than the symmetric tooth flanks. It makes it doable to cut back the helix angle and axial bearing load. For the self-locking gears that used to forestall inertial driving, totally different tooth flanks are used for driving and locking modes. On this case, uneven tooth profile with low-pressure angle gives excessive effectivity for driving mode and the alternative high-pressure angle tooth profile is used for dependable self-locking.

Testing Self-Locking Gears

Self-locking helical gear prototype units had been made based mostly on the developed mathematical fashions. The gear information are introduced within the Desk 1, and the take a look at gears are introduced in Determine 5.

The schematic presentation of the take a look at setup is proven in Determine 6. The 0.5Nm electrical motor was used to drive the actuator. An built-in pace and torque sensor was mounted on the high-speed shaft of the gearbox and Hysteresis Brake Dynamometer (HD) was linked to the low pace shaft of the gearbox by way of coupling. The enter and output torque and pace data had been captured within the information acquisition instrument and additional analyzed in a pc utilizing information evaluation software program. The instantaneous effectivity of the actuator was calculated and plotted for a variety of pace/torque mixture. Common driving effectivity of the self- locking gear obtained throughout testing was above 85 p.c. The self-locking property of the helical gear set in backdriving mode was additionally examined. Throughout this take a look at the exterior torque was utilized to the output gear shaft and the angular transducer confirmed no angular motion of enter shaft, which confirmed the self-locking situation.

Fig 5: Helical self-locking take a look at gears.

Potential Functions

Initially, self-locking gears had been utilized in textile trade [2]. Nevertheless, the sort of gears has many potential functions in lifting mechanisms, meeting tooling, and different gear drives the place the backdriving or inertial driving shouldn’t be permissible. One in every of such utility [7] of the self-locking gears for a constantly variable valve raise system was urged for an automotive engine.


On this paper, a precept of labor of the self-locking gears has been described. Design specifics of the self-locking gears with symmetric and uneven profiles are proven, and testing of the gear prototypes has proved comparatively excessive driving effectivity and dependable self-locking. The self-locking gears could discover many functions in varied industries. For instance, in a management programs the place place stability is essential (resembling in automotive, aerospace, medical, robotic, agricultural and so forth.) the self-locking will enable to attain required efficiency. Just like the worm self-locking gears, the parallel axis self-locking gears are delicate to working situations. The locking reliability is affected by lubrication, vibration, misalignment, and so forth. Implementation of those gears must be performed with warning and requires complete testing in all doable working situations.


1) Popper J.B. Cooperating Wedges together with mating worms, US Patent 2973660, 1961
2) Munster N.S., Tzarev G.V. Self-locking Cylindrical Gears, Idea Mechanisms and Machines, Publications of the Tashkent Polytechnic  Institute, 1968, #30A, 3 – 15. (in Russian)
3) Iskhakov T.G. Self-locking in Gear Mechanisms, Publications of the Kazan Aviation Institute, 1969, #105, Vol. 105, 3 – 15. (in Russian)
4) Timofeev G.A., Panukhin V.V. Self-locking Standards Evaluation, Vestnik Mashinostroenia, September 2003, 3 – 8. (in Russian)
5) Kapelevich A. L., Kleiss R. E., Direct Gear Design for Spur and Helical Gears, Gear Know-how, September/October 2002, 29 – 35.
6) Kapelevich A.L., “Geometry and design of involute spur gears with uneven enamel”, Mechanism and Machine Idea, 2000, Challenge 35, pp. 117-130.
7) Taye E., Actuator with self-locking helical gears for a constantly variable valve raise system, US Patent #US2009/0283062 A1 (pending).

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