On the Strength and Durability of Brake Rods in Mine Hoisting Machines
Abstract Generated abstract
This paper examines failures of brake rods in mine hoisting machines, where fatigue cracking, excessive tensile or compressive loading, lever-system misalignment, clearances, jamming, and brake-weight impacts can impair braking reliability. It proposes that periodic control tests evaluate rods for three conditions: fatigue resistance during service braking, resistance to plastic deformation during service or safety braking, and resistance to fracture under emergency loading. The authors develop calculation procedures using safety factors, stress-concentration and scale coefficients, dynamic and load-distribution factors, and material strength limits, with guidance for selecting coefficients when experimental data are unavailable. The method is presented both for assessing existing hoisting installations and for designing new machines, with low-carbon steels and avoidance of rod sections with holes identified as favorable for durability.
Full Text
On the Strength and Durability of Brake Rods of Mine Hoisting Machines
V. S. Udut, N. I. Klykov
(Presented by the Department of Occupational Safety and Mining)
Failure of the brake rods of mine hoisting machines is inevitably associated with partial or complete failure of the brake at the most critical moment of the hoisting operation: during normal and emergency stopping of the machine. This, in turn, can put the hoisting installation out of operation for a long time or lead to an accident.
Studies of the causes of failures of brake rods on hoisting machines in the Kuzbass have shown that in some cases the destruction of rods occurs because of the formation of fatigue cracks, while in other cases excessive tensile or compressive forces arise in the rods as a result of misalignment of the lever system, the presence of large clearances, jamming and dropping of the brake weight, etc. In some cases individual rods of the lever system underwent plastic elongation, which in turn led to misalignment of the brake shoes and even to failure of the brake segments.1
In view of the fact that the strength of brake rods is significantly affected by operating factors, it is proposed that, when conducting the biennial control tests of hoisting installations, the strength of the rods be checked for the following conditions: 1) resistance to fatigue failure during service braking; 2) resistance to plastic deformation during service or safety braking; 3) resistance to failure under emergency loading of the brake rods.
Checking the Strength of Brake Rods for Fatigue
The formation of fatigue cracks is the most frequent cause of failure of brake rods. During a normal stop of a machine using the brake, pulse tension or compression of the brake rods occurs—on average 6–12 pulses per one hoisting operation. During prolonged operation of a hoisting machine, the brake rods may experience millions of cycles of periodic loading. Fatigue cracks usually arise at locations of high local stresses—in rod sections with holes, transitions, grooves, threads, etc. It is clear that the local stresses must not exceed the fatigue limit (endurance limit) of the material under a pulsating loading cycle. But since fatigue tests of material specimens are usually carried out under a fully reversed symmetrical loading cycle, the endurance limit of the material under a fully reversed symmetrical cycle, $\sigma_{-1}$, is adopted as the strength criterion.
Experimental investigations have shown that the maxima of the stresses of the cycles are not identical. Therefore it is necessary to introduce a coefficient of averaging of the loading cycles, $K_{\mathrm{ц}}$, which represents the ratio of the average calculated maximum to the greatest maximum stress during service braking. Depending on the qualification of the operator, the brake system, and design and operating factors, the coefficient of averaging of the loading cycles varies from 0.6 to 0.9. On average, in the absence of experimental data, one may take $K_{\mathrm{ц}} = 0.8$.
The rods are calculated for durability by the formula
\[ n_{-1} = \frac{2 \xi_{\sigma} F_{0} \sigma_{-1}} {(K_{\sigma} + \varphi_{\sigma} \xi_{\sigma}) K_{\mathrm{ц}} P_{\max}} \leq [n_{-1}], \tag{1} \]
where
\[ \begin{aligned} n_{-1} &\text{ is the actual value of the endurance safety factor;}\\ [n_{-1}] &\text{ is the allowable value of the endurance safety factor;}\\ K_{\sigma} &\text{ is the effective coefficient of stress concentration}\\ &\text{ in the section under consideration;}\\ \varphi_{\sigma} &\text{ is a coefficient characterizing the sensitivity}\\ &\text{ of the material to cycle asymmetry;}\\ \xi_{\sigma} &\text{ is a coefficient accounting for the transverse dimensions}\\ &\text{ of the brake-rod sections (scale factor);}\\ F_{0} &\text{ is the area of the rod section allowing for weakening;}\\ P_{\max} &\text{ is the maximum force in the rod under consideration}\\ &\text{ during service braking.} \end{aligned} \]
For low-carbon steels, from which brake rods are usually made, the coefficient characterizing the sensitivity of the material to cycle asymmetry lies within the limits 0.05–0.1. The value of the scale factor, irrespective of the type of stress concentrator (excluding threads), may be taken as $\xi_{\sigma} = 0.6$–0.8. For threads, $\xi_{\sigma} = 0.5$–0.6. In both cases, larger values of the scale factor correspond to smaller transverse dimensions of the brake rods.
The maximum force in the brake rods is determined depending on the force developed by the brake drive (air or oil pressure on the piston in the cylinder of the service brake, or the weight of the brake load—in some designs), the transmission ratio and position of the corresponding levers, and the dynamic behavior of the brake system. In statically indeterminate brake systems, one must also take into account the nonuniformity of the distribution of forces in the corresponding brake rods. The coefficients of dynamic behavior and nonuniformity of distri-
...the distribution of forces in rods can be determined experimentally by oscillograph recording of the stresses in the rods. In the absence of experimental data, the following may be adopted: the dynamic coefficient during service braking \(K_{\text{d.r}}=1.1\); the coefficient of nonuniformity of force distribution in the rods \(K_{\text{nr}}=1.25\) (for a ratio of the smaller stress to the larger in the corresponding rods \(\lambda=0.8\)). The permissible value of the endurance reserve is
\[ [n_{-1}] = n_1 \cdot n_2 \cdot n_3, \tag{2} \]
where
\[ \begin{aligned} n_1 &= 1 \div 1.5 &&\text{is a coefficient characterizing the accuracy of accounting for the acting loads;}\\ n_2 &= 1.2 \div 1.5 &&\text{is a coefficient characterizing the plasticity of the material;}\\ n_3 &= 1.2 \div 1.5 &&\text{is a coefficient taking into account specific safety requirements.} \end{aligned} \]
If we take
\[ n_1=1.1; \qquad n_2=1.2; \qquad n_3=1.5, \]
then the permissible value of the strength reserve with respect to the endurance limit of the material will be
\[ [n_{-1}] = 1.1 \cdot 1.2 \cdot 1.5 = 2. \]
The effective stress-concentration coefficient in some cases can be determined directly from graphs or tables. For example, for sections of rods with threads, depending on the type of thread and the ultimate strength of the material \(\sigma_{\mathrm{в}}\), \(K_\sigma\) can be found from the following table:
| \(\sigma_{\mathrm{в}}\), kg/cm\(^2\) | \(K_\sigma\) for metric thread | \(K_\sigma\) for inch thread |
|---|---|---|
| 4000 | 3.0 | 2.2 |
| 6000 | 3.9 | 2.9 |
| 8000 | 4.8 | 3.5 |
In other cases the effective stress-concentration coefficient is determined according to A. N. Reshetov [1],
\[ K_\sigma = 1 + q(\alpha_\sigma - 1), \tag{3} \]
where
\[ \begin{aligned} q &\text{ is the coefficient of sensitivity of the material to stress concentration;}\\ \alpha_\sigma &\text{ is the theoretical stress-concentration coefficient.} \end{aligned} \]
The coefficient \(q\) depends on the radius of curvature of transitions, grooves, holes, and fillets in the rods, and on the ratio of the yield strength \(\sigma_{\mathrm{в}}\) to the ultimate strength of the material [2].
In brake-rod structures the radius of curvature in sections with stress concentrators is \(\rho > 10\) mm; therefore, depending on the above-mentioned mechanical characteristics of the material, the coefficient \(q = 0.65 \div 0.85\) (the smaller values apply to more ductile materials).
The theoretical stress-concentration coefficient \(\alpha_\sigma\) for different types of concentrators can be found from graphs [2, 3, 4]. According to these graphs, depending on the geometric dimensions of section elements, the theoretical stress-concentration coefficient for fillets, transitions, and grooves varies within the limits \(1.4 \div 2\), and
for sections with holes for rivets and bolts, 2.5–2.8. Obviously, designs of brake rods with holes are less durable and therefore undesirable [5]. On the basis of durability requirements, the best material for manufacturing brake rods is low-carbon steel—up to grade St. 35 inclusive.
Checking the Strength of Brake Rods for Resistance to Plastic Deformations
Both during service braking and during safety braking, the rods must not acquire residual elongations, which reduce the strength of the rods themselves and disturb the adjustment of the lever system. First it is necessary to establish under which braking the forces in the rods will be greatest. The method for determining the greatest forces acting in the rods during safety braking is analogous to that indicated above. But in this case the dynamic coefficient also depends on the nature of the damping of the forces when the brake weight falls. On the basis of experimental data, the following average values of the dynamic coefficient during safety braking \(K_{q.n}\) may be adopted: 1–1.1—hydraulic brake; 1.1–1.2—pneumatic brake; 1.3–1.5—oil and spring dampers; 2—a falling weight without pneumatic or hydraulic drive and damper.
Tests carried out on specimens simulating brake rods showed that, for all types of stress concentrators, independently of the rate of application of the loads (excluding impact), the strength of brake rods for resistance to plastic deformations may be checked by the formula
\[ n_t=\frac{\varepsilon_t \sigma_t F_o}{P_{\max}}\le [n_t], \tag{4} \]
where
\[ \begin{aligned} n_t &\text{— the actual factor of safety with respect to the yield point of the material;}\\ [n_t] &\text{— the permissible value of the factor of safety of the rods for resistance to plastic deformations;}\\ \varepsilon_t &\text{— the scale factor.} \end{aligned} \]
The value of the scale factor in strength calculation for plastic deformations is \(\varepsilon_t=0.75\div0.8\) (the smaller values are for rods with large transverse dimensions).
The permissible value of the factor of safety of rods with respect to resistance to plastic deformations is determined by formula (2).
Checking the Strength of Brake Rods for Failure under Emergency Loading
Brake rods must not fail under emergency loading, since otherwise it is impossible to stop the machine normally and avoid major breakdowns or an accident. Emergency loads on rods usually arise during safety braking with increased dynamic action (for example, when the brake weight hangs up and then breaks loose) or with abnormal distribution of forces between rods (in statically indeterminate systems with incorrect adjustment of rod lengths, when some rods are almost unloaded and others are overloaded twofold). When determining the maximum forces in the rods, in the first case one should take \(K_{q.n}=2\), and in the second case \(K_{n.r}=2\). The remaining coefficients are taken as usual. A less probable (though possible: the case at the “Kapitalnaya-1” mine of the “Osni-
[[unclear: end of a proper name]]”) is the case of hanging up and breakaway of the brake weight under a nonuniform distribution of forces in the rods, when \(K_{q\cdot n}=2,\ K_{\mathrm{н}\cdot\mathrm{р}}=2\). Such a case need not be taken into account in the calculation; however, the permissible value of the safety factor of the rods with respect to the material’s ultimate strength, also determined by formula (2), is then \([n_{\mathrm{в}}]\geq 2\).
Obviously, the actual safety factor of the rods against fracture is
\[ n_{\mathrm{в}}=\frac{\varepsilon_{\mathrm{в}}\sigma_{\mathrm{в}}F_{0}}{P_{\max}}\leq [n_{\mathrm{в}}], \tag{5} \]
where \(\varepsilon_{\mathrm{в}}\) is the size factor.
The value of the size factor in calculating rods for strength with respect to ultimate strength is \(\varepsilon_{\mathrm{в}}=0.9\div 0.95\) (the smaller value for rods with large transverse dimensions).
The presented method for checking the strength of brake rods may also be used in designing new machines, for which it is then necessary to establish the calculated values of the maximum forces acting in the rods during service and safety braking.
REFERENCES
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A. N. Reshetov. Machine Parts. “Mashinostroenie,” 1964.
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S. V. Serensen et al. Load-Carrying Capacity and Strength Calculations of Machine Parts. Mashgiz, 1963.
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G. Neuber. Stress Concentration. OGIZ, Gostekhizdat, 1947.
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M. M. Frocht. Photoelasticity. OGIZ, GITTL, 1948.
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G. N. Savin. Stress Concentration around Holes. OGIZ, 1951.
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On the cage hoist of the Severnaya mine of the Kemerovougol trust, the rods burst as a result of the formation of fatigue cracks. On the cage hoist of the Kirov mine of the Leninugol trust, rod failure occurred as a result of misalignment of the lever system. On the skip hoist of the Ziminka-Kapitalnaya mine, the upper rods underwent plastic elongation, which caused overloading and failure of the brake segments. ↩