Experimental Study of Dynamic Loads in Spur Gear Transmissions During Gear Wear
Abstract Generated abstract
This paper reports an experimental investigation of how tooth wear affects dynamic loads in a closed spur gear reducer. Dynamic tooth forces were measured directly without disassembling the reducer while test gears operated under constant speed, load, and lubrication conditions for 436 hours, reaching about 2 percent total linear wear. The results show that, within the wear range studied, the dynamic coefficient decreased from 1.73 to 1.38, with the largest reduction occurring during running-in, and pitting on the driven wheel did not noticeably alter this trend. The authors attribute the reduction in dynamic loading to wear-induced smoothing of base pitch errors and running-in of tooth profiles, while noting that larger wear or damage involving seizure or plastic deformation could change the behavior.
Full Text
EXPERIMENTAL STUDY OF DYNAMIC LOADS IN SPUR CYLINDRICAL GEARS DURING WHEEL WEAR
S. I. SHUBOVICH, I. G. VOLKOV
(Presented by the scientific seminar of the Department of Applied Mechanics)
Studies of the wear of spur cylindrical gears [1] have shown that the transmission remains serviceable even with considerable wear of the wheel teeth. The bending strength of teeth, investigated by a number of authors under static conditions, does not decrease noticeably up to 20% wear of the wheels. However, in order to assess the bending strength of worn wheels under the operating regime of a reducer, it is necessary to clarify the qualitative picture of the dynamic processes in worn tooth meshes and to quantitatively evaluate the share of the dynamic component of the force acting on a tooth. Dynamic forces in a spur gear constitute a significant part of the load received by the teeth during meshing. There is no doubt that wear, by changing the geometry of the tooth profile, will affect the dynamics of the worn mesh.
In order to determine the pattern of variation of dynamic loads in a closed spur gear, we carried out an experiment involving their direct measurement as the wheels wore.
The method for studying dynamic forces took into account the influence of wear only. All other factors (speeds, loads, lubrication conditions, etc.) remained constant throughout the entire experiment. It should be emphasized that the experiment was conducted without disassembling the reducer. The research method is described in greater detail in the article included in the present collection.
In the experiment described, experimental wheels with the following characteristics were studied:
module \(m = 5\) mm;
number of teeth \(z_1 = 22,\ z_2 = 22\);
pressure angle \(\alpha^{\circ} = 20^{\circ}\);
face width \(b = 10\) mm;
material — steel 45;
hardness 160 \(HB\) without heat treatment;
manufacturing accuracy, grade 8х according to GOST 1643;
surface finish of the profile — class 6.
The transmission operated for wear in a closed reducer without an abrasive medium, under a load twice the design load with respect to contact strength. The design contact load was determined by the method of V. N. Kudryavtsev [2].
In the experiment carried out, the reducer operated for 436 hours; the total linear wear of the pair of teeth under study reached 2% by the end of the experiment.
During this period, 8 measurements of wear, dynamic forces, and sensor calibrations were performed.
The wear curves (Fig. 1) have a typical form, with a clearly expressed running-in period and a subsequent monotonic increase in wear with an increase in the number of loading cycles. It is interesting to note the circumstance that, with equal hardnesses of the experimental wheels and a gear ratio of the transmission \(i = 1\), the wear of the pinion is ahead of the wear
Fig. 1. Graph of wheel wear and change in total tooth force: 1 — wear of the driving wheel; 2 — wear of the driven wheel; 3 — total wear of the wheels; 4 — total forces on the tooth under study \(P\)
of the driven wheel. The noted phenomenon can be explained if one takes into account the direction of the tangential friction forces determining wear on the driven wheel (always directed toward the pole) and on the driving wheel (directed away from the pole). In this case, conditions of erasing and removal of wear particles from the contact zone arise that are inherent only to gear meshing, more favorable for the driving wheel and worse for the driven one.
Wear delays the onset of pitting or prevents it altogether. Therefore, it was natural to expect pitting to occur on the driven wheel. We observed the occurrence of pitting on the teeth of the driven wheel at \(9.07 \cdot 10^6\) loading cycles. On the driving wheel, pitting was absent. No noticeable increase in wear after the onset of pitting was observed.
In Fig. 1, for clarity, a curve is shown for the change in the full maximum tooth force \(p\) as a function of wear time. Since a change in this force is possible only due to impact loading at a constant torque on the reducer shafts, the detected regularity is also valid for the dynamic component of the force.
The main regularities in the change of dynamic forces as a function of the relative total wear \(\Delta U\) are presented in Fig. 2.
Within the limits of the wheel wear attained in the experiment, the dynamic coefficient \(K_{\mathrm{d}}\) decreased from 1.73 to 1.38. The averaged calculated value \(K_{\mathrm{d}}\), computed according to the method of A. I. Petrusevich, for wheels of this manufacturing accuracy was 1.5. The indicated value of \(K_{\mathrm{d}}\) in our experiment was recorded after running-in wear. With subsequent
with monotonic increase in wear, a tendency toward a further decrease in \(K_{\mathrm{d}}\) was observed.
In Figs. 1 and 2, the vertical dashed line marks the onset of spalling on the profile of the driven wheel. The spalling did not alter the general regularity of the meshing dynamics and did not slow the rate of decrease of \(K_{\mathrm{d}}\) as wear increased. A quantitative assessment of the dynamic component and of the total force on the tooth as a function of wear is given by curves 2 in Fig. 2.
Fig. 2. Graph of the variation of \(P\), \(P_{\mathrm{d}}\), and \(K_{\mathrm{d}}\) as a function of the total relative wear of the pair of teeth studied: 1—curve of variation of \(K_{\mathrm{d}}\); 2—curve of variation of \(P_{\mathrm{d}}\); 3—curve of variation of \(P\).
The mechanism of the observed phenomenon and of the regularities resulting from it in the influence of wear on meshing dynamics is explained by us for the following reasons. It has been shown experimentally by many authors that wear reduces the errors of the base pitch of the gearing. During re-engagements, the impact nature of the load on the tooth, caused by incorrect meshing due to unavoidable manufacturing errors, is softened as the difference between the errors of the base pitches and their absolute values decreases. In the intervals between re-engagements, the tooth surfaces, wearing in, automatically approach conjugate profile forms, although this profile, owing to nonuniformity along the length of the working portion of the profile, gradually deviates from the involute.
The explanation given above is valid for small wheel wear and if the wear is not accompanied by seizure and plastic deformations.
With large wear, in connection with the shortening of the length of contact and of the contact ratio, the picture may become different.
The qualitative picture of the course of the dynamic meshing process did not undergo noticeable changes as wear increased. A slight rise in the basic background of load oscillations was noted, which is explained by some shortening of the length of contact.
In conclusion, let us estimate the errors in measuring the load on the tooth. If the phase error is taken as the error criterion
of the apparatus, \(\Delta \Phi\), regarding it as a measure of the deviation of the real phase characteristic from the linear one, it can be calculated [3]:
\[ \Delta \Phi = \left[ \left( 1+\frac{1}{3m_{1:2}^{2}}+\frac{1}{5m_{1:2}^{4}}+\cdots \right)-1 \right]100,\ \%, \]
where
\[ m_1=\frac{f_{\mathrm{н}}}{f_{\mathrm{п}}}; \qquad m_2=\frac{f_{\mathrm{ш}}}{f_{\mathrm{п}}}, \]
\(f_{\mathrm{п}}=1200\ \text{Hz}\) — frequency of the recorded process,
\(f_{\mathrm{ш}}=5\ \text{kHz}\) — natural frequency of the loop,
\(f_{\mathrm{н}}=10\ \text{kHz}\) — carrier frequency of the strain-gauge station.
It is borne in mind that phase distortions of the signal occur in stages—in the strain-gauge station and in the loop. The total error for the indicated frequency ratios is \(\Delta \Phi = 2.3\%\), i.e., it lies within the certified errors of the apparatus.
Conclusions
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The dynamic loads at any stage of the wear achieved in the experiment did not exceed the dynamic loads arising in the meshing of new, unrun-in wheels. The greatest decrease in \(K_{\mathrm{д}}\) was observed during the period of running-in wear. As monotonic wear progresses, the dynamic factor decreases.
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With equal wheel hardnesses and a transmission gear ratio \(i=1\), wear of the driving wheel outpaces wear of the driven wheel. This phenomenon is due to the specific wear conditions inherent only in gear meshing.
REFERENCES
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Yu. S. Semenov. Study of the wear of gear wheels of mining electric-drill reducers. In: “Calculation, Design, and Investigation of Transmissions,” vol. III. Publishing House of the Odessa Polytechnic Institute, 1959.
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V. N. Kudryavtsev. Simplified Calculations of Gear Transmissions. Mashgiz, Moscow–Leningrad, 1960.
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I. A. Popov. On the possibility of nonlinear dynamic distortions in bridges of parametric transducers supplied with carrier-frequency current. In: “Experimental Methods for the Investigation of Machines.” Academy of Sciences of the USSR, 1954.