Introduction. Currently, there are 51,670 hazardous production facilities registered in the Russian Federation that operate more than 284,000 lifting devices, including 224,363 cranes. It's worth noting that 51.2% of these lifting devices have already reached the end of their standard service life.

In 2023, there were 30 recorded accidents at lifting facilities. The analysis of causes of accidents over the past few years has revealed that the main contributing factors are: poor production control [1], operation of faulty lifting structures, and inadequate organization of inspections, maintenance, and scheduled repairs for lifting structures [2].

The sanctions imposed by producing countries have affected foreign lifting cranes that are mainly used in sea and river ports. For many imported lifting cranes, their service life has reached a critical point or exceeded the established standard [3]. To ensure the safe operation of these devices in accordance with the regulatory legal acts of the Russian Federation, an industrial safety inspection is required. This mandatory step ensures the reliability and safety of crane operation and compliance with applicable standards and regulations. The classification groups, classes of use, and loading modes for these cranes are based on the international European standard FEM 1.001-19981 “Rules for the Design of Hoisting Appliances”, which is equivalent to the Russian standard GOST 34-017-20162. A comparative analysis of these regulatory documents has shown that, according to FEM3, the crane loading is indicated as Q2 in the certificate, while the actual load corresponds to Q3. This results in an excess of the classification group value and increased risk of accidents.

The main challenge of operating such cranes in the context of sanctions imposed by manufacturing countries is the termination or severe restriction of the supply of equipment, spare parts, and assemblies for these cranes, as well as disruption of contact for consulting services related to their operation. Additionally, there has been a cessation of equipment maintenance by specialists from supplier companies, as well as remote monitoring of equipment status and updates to software products that ensure the safe operation of the cranes.

Jib cranes, in accordance with the legislation of the Russian Federation No. 116 FZ4, belong to potentially dangerous objects of hazard class IV, and must comply with standard safety requirements, such as reliability, durability, maintainability, and safety [4][5].

During the scheduled expert inspections of cranes, the presence of separate resource-determining (resource-limiting) components and elements of metal structures was established [6]. Damage (resource depletion) of such components can lead to the complete destruction of the structure. For example, there have been accidents related to: the destruction of the rail attachment unit of the boom outreach mechanism for an Albatross type portal jib crane (Fig. 1), the destruction of the outrigger attachment unit for a tower crane (Fig. 2), the destruction of the lifting mechanism for a portal jib crane (Fig. 3).

The described accidents have a common cause, which is exceeding the crane's classification group (mode) of the specified value in the passport, which in turn leads to exceeding the service life for the crane as a whole and the resource-determining components of the crane specifically.

The task of conducting an objective assessment of the technical condition of jib cranes during the process of industrial safety inspection is essential. Therefore, the aim of this work was to develop a methodology for determining the actual classification group (mode) of jib cranes of foreign companies and to test the developed methodology using a specific example.

Materials and Methods. Gottwald type cranes have an A5 or A6 crane operating mode classification group with recommended parameters according to International European standards FEM 1.001–19985 [8]:

With these parameters, the expected lifetime of the components and mechanisms [9] of the crane must be achieved, expressed in operating hours (Table 1).

This table determines the recommended service life in operating hours for the bearing metal structures of cranes, as well as for the main components of the crane — lifting, rotating, chassis, electrical, and hydraulic equipment — under a specific loading mode Q. For instance, the service life of a crane's metal structure under loading mode Q2 was 40,000 operating hours.

According to FEM6, Q2 load mode is recommended for imported cranes. However, when we analyzed the actual load on several cranes that were surveyed, we found that the current load mode corresponded to Q3 level, which exceeded the passport values for the crane's classification group [10].

When conducting an industrial safety inspection, it is essential to collect data on the actual loading of the crane [11]. However, it is not always possible to use parameter recorders, as they may not be operational. Therefore, in such situations, it was decided to use statistical data on the actual loading of cranes.

Loading of jib cranes is a function of at least two parameters — the load weight and the boom outreach, the product of which determines the load moment. In general, these parameters can be random values [12]; they should be taken into account when determining the crane load.

Therefore, the key task of determining the classification group (mode) of the crane is to gather initial data and construct histograms of the distribution of transported cargo masses and boom outreach of the crane under test. The distribution of random variables (the mass of the transported goods and the boom outreach of the crane) is characterized by such quantities as the average value (mathematical expectation) and the standard deviation (variance).

Let us take the random values distribution law (the mass of the transported goods and the boom outreach of the crane) as normal, which will greatly simplify calculations in the future [13]. The accepted assumptions are supported by studies of the boom outreach and angle of inclination of portal jib crane presented in [7][8].

Results. In order to obtain more objective information to make an informed decision on further operation of jib cranes of foreign companies, a methodology has been developed for assessing the actual classification group (mode) for conducting an industrial safety inspection. The process included several stages. The first step was to determine the actual value of the load distribution coefficient Кр through the load moments and compare it with the passport value. The second stage included an assessment of the remaining operating life and its comparison with the standard value. Then, the maximum fatigue stresses of the resource-determining unit of the metal structure were calculated, followed by a comparison of the obtained value with the limit value. The probability of structural failure was also calculated and compared with the acceptable value. An important element of the assessment was the analysis of the accident risk level.

As an example, we considered a specific case where the actual classification group (mode) of a jib crane was determined and it was recommended for decommissioning. At the first stage, the load distribution coefficient Кр was determined in terms of load moments from the expression:

(1)

where Ci/CT — ratio of the number of operating cycles of a crane with an average load torque to the total number of cycles (we assumed 1 in calculations); М(xy) — mathematical expectation of the load moment; Мn — maximum load moment of the crane specified in its certificate; Мxy = 28×40 = 1,120 t∙m; Мn = 33.4×50=1,670 t∙m (40 and 50 — average and highest outreach value in the hook mode; 28.0 and 33.4 — average and highest lifting capacity of the crane in the hook mode according to cargo characteristics).

(2)

According to [5][6][9], the crane classification group (mode) is generally determined depending on the class of use (U0 – U9), characterized by the maximum number of cycles per service life, and the loading mode (Q1–Q4). Calculated value of the load distribution coefficient Кр = 0.30 corresponded to A6 classification group (mode) of the crane as a whole, but was higher than A5 nominal value [14].

At the second stage, the residual life of the crane was estimated based on the current value of the characteristic number, which was a measure of the crane's life, and was determined taking into account the load distribution coefficient of the crane for the corresponding loading mode and the number of operating cycles [15].

The limiting condition of the crane in terms of operating time occurred if the current characteristic number was equal or higher than the standard value. The residual life was calculated using the following equation:

(3)

where Nн — standard value of the characteristic number, which was determined by the crane's classification group and operating mode according to [9][10]; Nт — current value of the characteristic number.

(4)

For the example discussed earlier, the additional conditions were as follows:

Nн = 125,000 — standard value of the characteristic number for A5 crane classification group (mode);

С = 596,228 — estimated number of working cycles;

Then the current value of the characteristic number was:

Nт = 596,228×0.67³ =179,323;

179,323 > 125,000;

Nт > Nн .

Conclusion: the resource was exhausted.

At the next stage, a verification calculation of the resource-determining assembly of the metal structure [11] for fatigue resistance was performed according to the formula.

(5)

where smax — maximum stress; av — coefficient of the operating mode of the element; RV — calculated fatigue resistance calculated considering time resistance, steel, and the group of elements' joints, taking into account the degree of stress concentration; gv — coefficient that took into account the type of stress state and the asymmetry of operating stresses;gс — coefficient of operating conditions.

The value of operating mode coefficient av was determined based on the crane's operating mode group and the level of stress concentration. The value gv was calculated based on the type of stress state and the stress asymmetry coefficient:

(6)

where smin and smax — maximum and minimum absolute stresses in the calculated element.

As an example, we calculated the reference contour of the rotary device on a portal jib crane. The results of this calculation can be found in Table 5, which shows the fatigue resistance.

The verification calculation of the reference contour of the portal jib crane's rotary device for fatigue resistance indicated that the maximum stress values calculated were close to the limiting value.

Based on the statistical data on the load of the jib crane, we could determine the probability of destruction of the resource-determining element of the metal structure using the following expression:

(7)

where Ф(х) — Laplace function; σн — average square deviation of stresses in the distribution of the load factor; σп — average square deviation of stresses in the distribution of the strength factor; σvср — average calculated stress in the structure; σпср — average value of the fatigue limit of the structural material, taking into account the cycle asymmetry; σк — calculated stress value at the intersection point of the alternating stresses distribution of and the distribution of fatigue limits, which could be obtained from solving the equality of load and strength distribution equations. Table 6 provides the calculation results.

The safety condition was not fulfilled, because the calculated value of the probability of destruction equal to 2×10–3 exceeded the permissible value of 10–4.

For comparison, Table 7 shows the failure probabilities of jib-type crane elements.

At the final stage, based on regulatory and technical documentation, a risk assessment was conducted to determine the level of safety for further operation of the jib crane. The background risk of accidents for lifting cranes was calculated using statistical data from the last 27 years:

Table 8 presents the damage from accidents at hazardous production facilities with lifting cranes, including direct losses, costs for localizing and mitigating the consequences, and economic losses based on statistical data from open press sources.

For comparison, Table 9 provides information on the probability of events with other types of equipment operated at hazardous production facilities.

Discussion and Conclusion. Using a specific example, the results showed that exceeding the crane's classification group (mode) and the assigned crane resources as a whole, including structural elements that determine the resource, will inevitably increase the risk of accidents involving jib cranes. Therefore, it was determined that the actual classification group of the crane was A6, which exceeds the passport value A5.

The developed methodology for assessing the actual classification group (mode) of jib cranes of foreign companies will significantly reduce the likelihood of structural failure of jib cranes and the level of accidents during industrial safety inspections. Currently, in Russia, the acceptable level of risk is determined qualitatively without specific numerical values for the probability of accidents or the amount of damage. The numerical values of the probability of accidents and the amount of damage are determined based on the economic and social development of society and may vary depending on the industry. Therefore, it is recommended to use the background probability of a lifting crane accident of 1.66·10-4 and an average material damage value of 73.2 million rubles in calculations.

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