RU2071116C1 - Device for determining optimal serviceability check intervals - Google Patents

Abstract

FIELD: computer engineering; inspection devices for research and engineering purposes where optimal serviceability check and control intervals are to be determined for parts functioning with availability not less than that specified at minimal possible average unproductive life expenditure. SUBSTANCE: device has time sensor 2, nonlinearity unit 1, adders 8,10,19, multiplication units 5,6,7,9,20,21, subtracters 4,18, division units 11,12, delay element 13, integrator 14, OR gate 23, comparators 14,22, switches 15,16,17. Advantage of proposed device is that it can determine optimal serviceability check and control intervals for equipment functioning with availability not less than specified value at the same time having minimal possible average unproductive expenditure of service life in the course of operation; in addition, it enables determining average quantity of spare parts required to ensure normal functioning of equipment within desired time period. EFFECT: enlarged functional capabilities due to control of equipment serviceability. 1 dwg

Description

 The invention relates to the field of computer technology, in particular to control devices, and can be used in scientific research and technology, where it is required to find the optimal time to start monitoring and controlling the technical condition of the product, functioning with a availability factor of at least a given value with the lowest possible average value of unproductive consumption resource.

 The aim of the proposed invention is to expand the scope of the device by controlling the technical condition of the product, functioning with a availability factor of at least a given one and having at the same time the minimum possible average value of unproductive consumption of a resource, and determines the average number of backup elements necessary for normal operation of the product.

 Operating experience of products for various purposes indicates the need for monitoring and control of the technical condition (maintenance) of these products at all stages of operation. One of the main parameters of the service strategy is the monitoring period, the value of which is advisable to find out of considerations of the required readiness of the product for intended use.

где

среднее время цикла обслуживания;

среднее время работоспособного состояния изделия между сеансами обслуживания.An important characteristic of product availability is the availability factor, which in general can be determined by the formula

Where

average service cycle time;

the average working time of the product between maintenance sessions.

где P(τ)=exp[-λt] вероятность безотказной работы на интервале времени между сеансами контроля;

интенсивность отказов;
τ_o среднее время нахождения изделия в состоянии скрытого отказа;

среднее время восстановления работоспособности изделия. считаем, что обслуживание изделия осуществляется только в плановые сеансы. Интервал времени между этими сеансами период обслуживания и его значение составляет

Среднее время

работоспособного состояния на периоде обслуживания определим по формуле

Подставив (2), (3), (4) в (1), получим

Из (5) видно, что коэффициент готовности функция от периода обслуживания. Чем раньше будет обнаружен и устроен отказ, тем больше будет доля времени, в течение которого изделие работоспособно и, следовательно, больше будет коэффициент готовности. Исходя из этого, можно говорить о зависимости коэффициента готовности от периода контроля работоспособности изделия K_г(τ). Эту функция, как показывают исследования, является монотонно убывающей и достигает своего максимума при τ= 0, т. е. при постоянном контроле. Однако для большинства изделий по экономическим или техническим причинам такое обслуживание нецелесообразно. Поэтому в большинстве случаев используют дискретный контроль. Для обеспечения требуемой готовности назначения имеется некоторое заданное значение K $\genfrac{}{}{0ex}{}{\text{3}}{\text{г}}$ коэффициента готовности. Интервалы τ между моментами времени, существенными с точки зрения оценки технического состояния изделия, определяются интенсивностью отказов и заданным значением коэффициента готовности. Поэтому на различных этапах функционирования изделий период контроля работоспособности может быть различным. В связи с этим задачу поиска периода, обеспечивающего функционирование изделия с коэффициентом готовности не менее заданного, можно записать, используя (5), следующим образом

Существует широкий класс изделий, которые в процессе функционирования расходуют некоторые материальные ресурсы (ресурсы "жизнедеятельности"), причем запас таких ресурсов ограничен.The value of the availability factor at any time during the operation of the products significantly depends on the period of service and on the intensity of failures. At interval T, _{from a} given time of operation, the product may be in an operable state of latent failure, control, and restoration of operability. There are many products whose performance monitoring is unchanged. It is carried out during the operation of the product, without interfering with its functioning as intended. For such products, the average cycle time will be

where P (τ) = exp [-λt] the probability of failure-free operation in the time interval between monitoring sessions;

failure rate;
τ _{o the} average time spent by the product in a state of latent failure;

average recovery time of the product. We believe that product service is carried out only in scheduled sessions. The time interval between these sessions is the maintenance period and its value is

Average time

a healthy state during the service period is determined by the formula

Substituting (2), (3), (4) into (1), we obtain

From (5) it is seen that the availability factor is a function of the service period. The earlier a failure is detected and arranged, the greater will be the fraction of the time during which the product is operational and, therefore, the availability factor will be greater. Based on this, we can talk about the dependence of the availability factor on the period of monitoring the health of the product K _g (τ). This function, as studies show, is monotonically decreasing and reaches its maximum at τ = 0, i.e., with constant monitoring. However, for most products, for economic or technical reasons, such maintenance is not practical. Therefore, in most cases, discrete control is used. To ensure the desired availability of the assignment, there is some setpoint K $\genfrac{}{}{0ex}{}{\text{3}}{\text{g}}$ availability factor. The intervals τ between time points that are significant from the point of view of assessing the technical condition of the product are determined by the failure rate and the specified value of the availability factor. Therefore, at various stages of the functioning of the products, the period of monitoring the performance may be different. In this regard, the task of finding a period that ensures the functioning of the product with a availability factor of at least a given can be written using (5) as follows

There is a wide class of products that in the process of functioning consume some material resources (resources of "life"), and the supply of such resources is limited.

We introduce the following notation:
R is the value of a limited resource;
C _f average resource consumption per unit time when the product is in a healthy state;
C _{about the} average resource consumption per unit time when the product is in a state of failure;
R _{to the} resource consumed as a result of one session of monitoring the health of the product;
R _{in the} resource spent on restoring the product in the event of a failure.

где N число сеансов обслуживания

можно записать выражение для величины среднего непроизводительного расхода ресурса в виде

с учетом (8), (9)

В связи с изложенным, актуальной задачей является определение оптимального периода обслуживания изделий, обеспечивающего минимум непроизводительного расхода ресурса "жизнедеятельности" и функционирование изделия с коэффициентом готовности не менее заданного. Эта задача может быть записана в следующем виде:

С учетом (6) и (10) задача (11) приобретает вид

Наряду с этим, важной задачей является обеспечение требуемой надежности изделия при известной стратегии его обслуживания. Одним из путей обеспечения надежности изделия является резервирование. В связи с этим требуется знать число резервных элементов, необходимых для безотказного функционирования изделия в процессе эксплуатации (кратность резервирования).The following balance sheet holds.

where N is the number of service sessions

we can write the expression for the value of the average unproductive consumption of a resource in the form

taking into account (8), (9)

In connection with the above, an urgent task is to determine the optimal period for servicing products, ensuring a minimum of unproductive consumption of the resource "life" and the functioning of the product with a availability factor of at least a given. This task can be written as follows:

Taking into account (6) and (10), problem (11) takes the form

Along with this, an important task is to ensure the required reliability of the product with a known strategy for its maintenance. One way to ensure product reliability is redundancy. In this regard, it is required to know the number of spare elements necessary for the trouble-free operation of the product during operation (redundancy ratio).

с учетом (8)

При данной математической модели нахождения оптимального периода контроля и управления состоянием изделия, среднего значения непроизводительного расхода ресурса и числа резервных элемент может быть реализован аппаратурно с помощью предлагаемого устройства.The number of backup elements is found from the ratio

subject to (8)

With this mathematical model of finding the optimal period for monitoring and controlling the state of the product, the average value of unproductive consumption of the resource and the number of backup elements can be implemented in hardware using the proposed device.

 The drawing shows a diagram of a device.

 The device comprises a non-linearity unit 1, a time sensor 2, an integrator 3, a first subtractor 4, a first multiplication unit 5, a second multiplication unit 6, a third multiplication unit 7, a first adder 8, a fourth multiplication unit 9, a second adder 10, a first division unit 11, second division block 12, delay element 13, first comparator 14, first 15, second 16, third 17 keys, second subtractor 18, third adder 19, fifth multiplication block 20, sixth multiplication block 21, second comparator 22, OR element 23.

 The device operates as follows.

 In block 1 of nonlinearity, the value of the coefficient λ in the exponent exponent exp (-λt) is set by the magnitude of the signal from the fifth input of the device.

среднего времени восстановления работоспособности изделия. Сигнал

с выхода третьего блока 3 умножения поступает на первый вход сумматора 8. Значение сигнала

поступает на вход делителя первого блока деления 11. Значение сигнала

с выхода интегратора 3 поступает на вход вычитаемого первого вычитателя 4, на второй вход первого блока 5 перемножения и на вход делимого первого блока 11 деления. Значение сигнала

поступает на вход второго компаратора 22. Значение сигнала

- среднее время нахождения изделия в состоянии скрытого отказа с выхода первого вычитателя 4 поступает на один вход второго блока 6 умножения, на другой вход которого с входа устройства поступает значение C_о средний расход ресурса в единицу времени при нахождении изделия в состоянии отказа. На первый вход первого блока 5 перемножения с входа устройства поступает значение сигнала C_ф среднего расхода ресурса в единицу времени при нахождении изделия в работоспособном состоянии. На первый вход третьего блока 7 умножения поступает значение сигнала R_в ресурс, расходуемый на восстановление работоспособного состояния изделия в случае обнаружения отказа. Сигнал R_в[1-P(t)] с выхода третьего блока 7 умножения поступает на один вход сумматора 10, на другой вход которого с входа устройства поступает значение сигнала R_к ресурса расходуемого в результате проведения одного сеанса контроля работоспособности изделия, на третий вход которого поступает с выхода второго блока 6 умножения значение сигнала

. Значение сигнала R_к + R_в[1-P(t)] + C_ot_o с выхода сумматора 10 поступает на первый вход шестого блока 21 умножения, и на один вход третьего сумматора 19 на другой вход которого с выхода первого блока умножения 5 поступает значение сигнала

. Значение сигнала

с выхода третьего сумматора 19 поступает на вход делителя второго блока деления 12, на вход делимого которого с входа устройства поступает значение сигнала R ограниченного ресурса. Значение сигнала

с выхода второго блока деления 12 поступает на вход шестого блока умножения 21 и на вход пятого блока перемножения 20. Значение сигнала

среднего числа резервных элементов поступает на информационный вход первого ключа 15. Значение сигнала:

с выхода шестого блока 21 умножения поступает на информационный вход второго ключа 16, на первый вход первого компаратора 14 и через элемент задержки 13 на второй вход первого компаратора 14. В первом компараторе 14 происходит сравнение двух сигналов C_ф(t) и C_ф(t-Δt). Как только в момент времени t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ значение сигнала C_ср(t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ ) превысит значение C_ср(t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ -Δt), на выходе первого компаратора 14 вырабатывается сигнал, который поступает на вход элемента ИЛИ 23. Во втором компараторе 22 происходит сравнение значений K_г(t) и K $\genfrac{}{}{0ex}{}{\text{3}}{\text{г}}$ , как только в момент времени

станет меньше или равно K $\genfrac{}{}{0ex}{}{\text{3}}{\text{г}}$ , с выхода второго компаратора 22 выдается управляющий сигнал на первый вход элемента ИЛИ 23. При поступлении сигнала от одного из компараторов на выходе элемента ИЛИ формируется управляющий сигнал. Управляющий сигнал на выходе элемента ИЛИ 23 появится в момент времени t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ , если t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ <t $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ , либо в момент времени t $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ , если t $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ <t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ . Этот управляющий сигнал поступает на управляющие входы первого 15, второго 16 и третьего 17 ключей. В результате чего на третьем выходе устройства будет значение τ^*=t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ ∨t $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ оптимального периода контроля и управления техническим состоянием изделия, функционирующего с коэффициентом готовности не менее заданного при минимально возможном среднем значении непроизводительного расхода ресурса. На втором выходе устройства будет минимальное среднее значение C $\genfrac{}{}{0ex}{}{\text{*}}{\text{ср}}$ =C_ср(τ^*) непроизводительного расхода ресурса изделия при обслуживании его периодом τ^*. На первом выходе устройства будет среднее значение

числа резервных элементов, необходимых для нормальной эксплуатации изделия при обслуживании его периодом τ^*.The value of the signal P (t) of the probability of failure-free operation from the output of block 1 of nonlinearity is fed to the input of the integrator 3 and the input of the subtracted second subtractor 18, to the input of which is reduced a single signal is supplied. The value of the current time from the output of the sensor 2 (generator of linearly varying voltage) is fed to the input of the reduced first subtractor 4, to the input of the first adder 8 and to the information input of the third block 17 of the result. The value of the signal 1 P (t) from the output of the second subtractor 18 is input to the third block of multiplication 7, to the second input of the fifth block of multiplication 20 and to the second input of the fourth block 9 of multiplication, the first input of which is the signal value

average recovery time of the product. Signal

from the output of the third block 3 multiplication is supplied to the first input of the adder 8. The signal value

goes to the input of the divider of the first block of division 11. The value of the signal

from the output of the integrator 3 goes to the input of the deductible first subtractor 4, to the second input of the first block 5 of multiplication and to the input of the dividend first block 11 division. Signal Value

goes to the input of the second comparator 22. Signal value

- the average time the product is in a state of latent failure from the output of the first subtractor 4 is supplied to one input of the second multiplication unit 6, the other input of which from the device input receives the value C _{about the} average resource consumption per unit time when the product is in the state of failure. At the first input of the first block 5 multiplication from the input of the device receives the signal value C _{f the} average consumption of a resource per unit time when the product is in a healthy state. At the first input of the third block 7 of the multiplication receives the value of the signal R _{in the} resource spent on restoring the healthy state of the product in case of failure. The signal R _in [1-P (t)] from the output of the third multiplication unit 7 is fed to one input of the adder 10, to the other input of which from the input of the device the signal value R goes _{to the} resource consumed as a result of one session of monitoring the product’s health, to the third input which comes from the output of the second block 6 multiplication signal value

. The value of the signal R _to + R _in [1-P (t)] + C _o t _o from the output of the adder 10 is supplied to the first input of the sixth multiplication unit 21, and to one input of the third adder 19 to the other input of which is from the output of the first multiplication unit 5 signal value arrives

. Signal Value

from the output of the third adder 19 is fed to the input of the divider of the second division unit 12, to the input of the dividend of which from the input of the device the signal value R of the limited resource is supplied. Signal Value

from the output of the second division unit 12 is fed to the input of the sixth multiplication unit 21 and to the input of the fifth multiplication unit 20. Signal value

the average number of backup elements is supplied to the information input of the first key 15. Signal value:

from the output of the sixth multiplication unit 21, it goes to the information input of the second key 16, to the first input of the first comparator 14 and through the delay element 13 to the second input of the first comparator 14. In the first comparator 14, two signals C _f (t) and C _f (t -Δt). As soon as at time t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ signal value C _cf (t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ ) will exceed the value of C _av (t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ -Δt), at the output of the first comparator 14, a signal is generated that is fed to the input of the OR element 23. In the second comparator 22, the values of K _g (t) and K are compared $\genfrac{}{}{0ex}{}{\text{3}}{\text{g}}$ as soon as at time

will be less than or equal to K $\genfrac{}{}{0ex}{}{\text{3}}{\text{g}}$ , from the output of the second comparator 22, a control signal is issued to the first input of the OR element 23. When a signal is received from one of the comparators, a control signal is generated at the output of the OR element. The control signal at the output of the OR element 23 will appear at time t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ if t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ <t $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ or at time t $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ if t $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ <t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ . This control signal is supplied to the control inputs of the first 15, second 16 and third 17 keys. As a result, on the third output of the device there will be a value τ ^* = t $\genfrac{}{}{0ex}{}{\text{*}}{\text{1}}$ ∨t $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ the optimal period of monitoring and control of the technical condition of the product, functioning with a availability factor of at least a given at the lowest possible average value of unproductive resource consumption. The second output of the device will be the minimum average value of C $\genfrac{}{}{0ex}{}{\text{*}}{\text{wed}}$ = C _av (τ ^* ) of the unproductive consumption of the product’s resource when servicing it with a period of τ ^* . The first output of the device will be the average value

the number of backup elements required for normal operation of the product when servicing it with a period of τ ^*

Claims (1)

 A device for determining the optimal period of monitoring the technical condition of the product, containing a time sensor, a delay element, the input of which is combined with the first input of the first comparator, and the output is connected to the second input of the first comparator, the output of the nonlinearity block is connected to the input of the integrator, the output of which is connected to the first input of the first the division unit, the second input of which is connected to the output of the first adder, the second input of which is connected to the output of the time sensor, the first, second, third and fourth multiplication blocks, you One of the last of which is connected to the second input of the first adder, the second and third adders are connected in series, the first and second inputs of the second adder are connected respectively to the outputs of the third and second multiplication units, the second input of the third adder is connected to the output of the first multiplication unit, the first inputs of the first, second , the third and fourth blocks of multiplication and the second division block are respectively the first, second, third, fourth and fifth inputs of the device, the output of the second division block is connected to the first the input of the fifth multiplication block, the outputs of the first, second and third keys are respectively the first, second and third outputs of the device, and the first inputs of the keys are interconnected, the first subtracter, characterized in that, in order to expand the scope by controlling the technical condition of the product, a second subtractor and an OR element are introduced into it, the output of which is connected to the first input of the first key, the output of the first division unit is connected to the input of the second comparator, the output of which is connected to the first input of the AND element And, the second input of which is connected to the output of the first comparator, the input of the nonlinearity block is the sixth input of the device, and the output is connected to the input of the second subtracter, the output of which is connected to the second inputs of the fourth, third, and fifth multiplication blocks, the output of the last of which is connected to the second input of the first key, the integrator output is connected to the first input of the first subtractor and the second input of the first multiplication block, the output of the time sensor is connected to the second inputs of the third key and the first subtractor, the output of which is connected to the second input of the second multiplication unit, the outputs of the second adder and the second division unit are connected to the inputs of the sixth multiplication unit, the output of which is connected to the second input of the second key, the output of the third adder is connected to the second input of the second division unit, the third input of the second adder is the seventh input of the device.