On the Loading of Gearboxes of Handheld Electric Drills During Durability Testing
Abstract Generated abstract
This paper examines how handheld electric drill gearboxes should be loaded during durability testing, particularly for drills used in coal mines where spindle torque varies with coal properties and manually applied feed force. It reviews earlier test practice based on indirect power measurements and equivalent constant loading, then argues that sudden cutter jamming during drilling produces short-term inertial torques that are not captured by such diagrams. Using an energy balance between rotating masses and drill rod torsion, with experimentally determined rod stiffness and inertia, the authors estimate overload moments several times greater than the motor overturning moment. They propose a revised durability test loading diagram that includes these brief but significant overloads, with cycle timing based on experimental drilling and auxiliary-operation data.
Full Text
ON THE LOADING OF GEARBOXES OF HANDHELD ELECTRIC DRILLS DURING DURABILITY TESTING
L. T. DVORNIKOV, V. V. BURKOV
(Presented by the scientific seminar of the Department of Applied Mechanics)
- Handheld electric drills are used in coal mines when drilling blast holes in coal and soft rock. Experimental studies of handheld electric drills in mines have made it possible to establish that the drilling rate depends directly proportionally on the applied feed force. Therefore, increasing the power of the motors of handheld drills can lead only to an increase in drilling productivity. However, from the standpoint of operation, restrictions are imposed on the magnitude of the power: first, by weight, and second, by the maximum permissible torque on the motor shaft, owing to the specific operating conditions of drills as hand tools.
In this respect, it is highly expedient to install drills on feeders with the necessary increase in motor power. However, under certain constrained conditions it is absolutely necessary to use handheld drills precisely, as the most maneuverable.
Thus, the magnitude of the torque transmitted by the gear reducer is determined by the power of the drill motor, taking into account the feed forces possible during manual operation.
- The magnitude of the torque on the drill spindle, and consequently on the gearbox, is constantly changing for a number of reasons, the chief of which are the heterogeneity of the physicomechanical properties of the coal in the seam and the continual fluctuation of the feed force created by the worker.
The qualitative and quantitative variation of the torque on the spindle has been determined by many researchers, but in all cases indirectly—by measuring the power consumed by the motor and then recalculating it. If one takes into account that the drill motor is a certain damping element, it may be said that the magnitude of the consumed power does not give an absolutely correct idea of the magnitude of the torque on the spindle and on the drill gearbox. The absence of data from measuring the torque directly in the gearbox does not make it possible to establish the true law of its variation over time for substantiating the load diagram of drills during durability testing. At present, the Department of Applied Mechanics is designing a special experimental drill that will make it possible to record the magnitude of the torque directly in the gearbox during the process of drilling blast holes.
- In the study of the gearboxes of hand drills in 1959, Yu. S. Semenov, on the basis of processing numerous experimental diagrams of the variation in drilling power during direct drilling, substantiated the load diagram shown in Fig. 1. According to this diagram, the load on the spindle varied according to a linear law from \(M_1\) to \(M_2\) with a frequency of 15 cycles per minute.
Fig. 1.
The tests were carried out both under variable load and under constant loads: the minimum \(M_1\), the maximum \(M_2\), and the equivalent load with respect to contact stresses \(M\), which was somewhat, by 5–10, higher than the nominal value.
The conclusion that, under variable loading, the nature of the wear process of gear wheels with a small difference in the hardnesses \([HR_c]\) of the mating teeth (55–60—40–45) is similar to the nature of the wear process of analogous gear wheels under equivalent loading, and that the amount of wear under variable loading and the slopes of the wear curves practically do not differ from the amount of wear and the slopes of the wear curves under equivalent loads, drawn by Yu. S. Semenov, made it possible to assert that the load diagram of Fig. 1 can be replaced by a diagram with a constant load equal to the equivalent load.
- A large number of examined diagrams of power variation during the operation of hand drills, and observations of their operation, show that, owing to cracking of the coal and for other reasons, during the drilling of almost every borehole there are cases of jamming—stopping—of the cutter. This leads to overturning of the motor and to significant loads on the gearbox.
At the moment when the cutter jams, all the stored kinetic energy of the rotating masses is expended in twisting the drill rod, that is,
\[ \frac{I_{\mathrm{pr}}\cdot \omega^2}{2}=\frac{c\cdot \varphi^2}{2}. \tag{1} \]
Here \(I_{\mathrm{pr}}\) is the moment of inertia, reduced to the spindle, of all rotating masses, \(kg\,cm\cdot sec^2\);
\(\omega\) is the angular velocity of spindle rotation, \(rad/sec\);
\(c\) is the torsional stiffness of the drill rod, \(kg\,cm/rad\);
\(\varphi\) is the angle of twist of the rod, \(rad\).
Formula (1) makes it possible to determine the possible angle of twist of the drill rod.
The magnitude of the moment of inertia forces acting on the gearbox in the event of a sudden stoppage of the cutter is
\[ M_{\text{in}} = c \cdot \varphi . \tag{2} \]
The stiffness of the helical drill rod was determined experimentally on an Amsler-Laffon torsion machine by the “mirror and scale” method. A rod 0.9 m long has a stiffness of 8500 kg·cm/rad, and a two-meter rod, respectively, 18900 kg·cm/rad. The reduced moment of inertia is calculated from known formulas. The moment of inertia of the drill rod was determined experimentally on a monofilament suspension. With a rod length of 2 m it is equal to 0.0051 kg·cm·s²; with a length of 0.9 m, 0.0025 kg·cm·s². The moments of inertia forces determined by formula (2) proved to be very considerable: for \(e = 2\) m, \(M_{\text{in}} = 3420\) kg·cm; for \(e = 0.9\) m, \(M_{\text{in}} = 2340\) kg·cm, for an ER-18D drill with an ER-18D-20 gearbox. These moments many times (5–7 times) exceed the overturning moment of the motor and must necessarily be taken into account when testing drill gearboxes.
Fig. 2.
- On the basis of what has been set forth above, we compiled a loading diagram for drills when testing their gearboxes for durability, Fig. 2, taking into account possible short-term moments caused by a sudden stoppage of the cutter.
The time of the individual elements of the cycle and of the entire cycle was determined on the basis of processing a large body of experimental material on drilling rates, shot-hole depths, and the time of auxiliary operations (transition from the drilled shot-hole to the adjacent one). The overload time, determined from the differential equation of rotational motion, does not exceed 0.002 s.