From 74491aaf3dac6284ec08fac0d1ac6a739312c6de Mon Sep 17 00:00:00 2001 From: Mark Voltov Date: Fri, 12 Jan 2024 13:08:42 +0000 Subject: [PATCH] =?UTF-8?q?=D0=94=D0=BE=D0=B1=D0=B0=D0=B2=D0=BB=D0=B5?= =?UTF-8?q?=D0=BD=20=D0=BE=D0=B1=D0=B7=D0=BE=D1=80=20=D0=B3=D0=B8=D0=BF?= =?UTF-8?q?=D0=B5=D1=80=D0=B3=D1=80=D0=B0=D1=84=D0=BE=D0=B2=D0=BE=D0=B3?= =?UTF-8?q?=D0=BE=20=D0=BF=D0=BE=D0=B4=D1=85=D0=BE=D0=B4=D0=B0=20=D0=91?= =?UTF-8?q?=D0=BE=D0=B6=D0=BA=D0=BE=20=D0=90.=D0=9D.=20=D0=BA=20=D0=B4?= =?UTF-8?q?=D0=B5=D0=BA=D0=BE=D0=BC=D0=BF=D0=BE=D0=B7=D0=B8=D1=86=D0=B8?= =?UTF-8?q?=D0=B8?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../assembly-sequence-planning-overview.md | 85 ++++++++++++++++++ docs/technologies/img/AsmHypergraph.png | Bin 0 -> 55065 bytes .../img/DataStructureHypergraph.png | Bin 0 -> 80969 bytes .../img/HypergraphLinearisation.png | Bin 0 -> 28236 bytes 4 files changed, 85 insertions(+) create mode 100644 docs/technologies/img/AsmHypergraph.png create mode 100644 docs/technologies/img/DataStructureHypergraph.png create mode 100644 docs/technologies/img/HypergraphLinearisation.png diff --git a/docs/technologies/assembly-sequence-planning-overview.md b/docs/technologies/assembly-sequence-planning-overview.md index a81c803..964116a 100644 --- a/docs/technologies/assembly-sequence-planning-overview.md +++ b/docs/technologies/assembly-sequence-planning-overview.md @@ -45,6 +45,91 @@ title: 'Планирование последовательности сборк ## Обзор актуальных исследований + +### Гиперграфовый подход в декомпозиции сложных технических систем +__Божко А.Н. (2016-2019 гг.)__ + +Декомпозиция технической системы на сборочные единицы (СЕ) – одна из важных инженерных задач технической подготовки дискретного производства. На основе выбранной иерархии сборочных единиц формируются многие конструкторские и технологические документы: схема сборки, сборочного состава, разузлования, технологического членения и т.д. +Известно, что с вычислительной точки зрения – это труднорешаемая задача. Даже самая простая ее постановка – разбиение плоской фигуры на связные составные части – является NP-полной. Тем не менее, существуют различные подходы, призванные в той или иной степени упростить и автоматизировать решение данной задачи. +Одним из таких подходов является применение гиперграфов для декомпозиции сложных технических систем. Данный подход был предложен А.Н. Божко в ряде работ, где он описывает математический аппарат и обосновывает преимущества подхода применительно к задаче. + +Для описания подхода введем необходимые понятия: +Гиперграфом называется пара $H = (X, E)$, где $X$ – множество вершин, а $E$ – семейство подмножеств $X$, называемых гиперребрами. В общем случае, от обычного графа гиперграф отличается тем, что его гиперребра могут содержать в себе более двух вершин. + +![](img/DataStructureHypergraph.png) + +Важным понятием является базирование. + +__Базирование__ – это придание заготовке, детали или изделию требуемого положения относительно выбранной системы координат. + +__База__ – поверхность или заменяющее ее сочетание поверхностей, ось, точка, принадлежащая заготовке, детали или изделию, которая используется для базирования. + +__Конструкторская база__ – база, которая служит для базирования детали или сборочной единицы при сборке изделия. + +В работах Божко рассматриваются изделия, для которых сборочные операции соответствуют следующим требованиям: +1. Осуществляются механические связи между деталями (__когерентность__) +2. Могут быть выполнены при помощи двух независимых движений рабочих органов (__секвенциальность__) + +При этом фиксированное положение детали рассматривается как частный случай движения. Приспособление, используемое для закрепления детали, также является рабочим органом. + +![](img/AsmHypergraph.png) + +Чертеж изделия и гиперграф конструкции + +Корректной математической моделью механической структуры является __s-гиперграф__, т.е. гиперграф, который можно преобразовать в точку при помощи последовательности нормальных стягиваний. Нормальным стягиванием называется преобразование гиперграфа, заключающееся в отождествлении двух вершин ребра и удалении этого ребра. +При этом важно отметить, что поскольку СЕ должна соответствовать требованиям независимой собираемости, механическая структура СЕ описывается s-подграфом s-гиперграфа. + +Божко вводит ряд возможных ограничений, позволяющих формализовать и автоматизировать процесс построения гиперграфа сборки. Перечислим их: +1. Деталь не может входить в две и более СЕ +2. Гиперребро (а также ребро) входит в отдельную СЕ или соединяет различные СЕ +3. Любая СЕ содержит хотя бы одно ребро +4. Для СЕ должно выполняться линейное соотношение между числом вершин и связей гиперграфа +5. Если гиперребро (а также ребро) включено в состав СЕ, то все его инцидентные вершины должны войти в данную СЕ. Верно и обратное +6. Разбиение не может быть тривиальным, должна быть хотя бы одна невырожденная (содержащая более одного элемента) СЕ +При этом, конструктор может налагать ряд дополнительных ограничений исходя из специфики объекта: +1. Некоторые детали входят в одну СЕ +2. Некоторая пара деталей не входит в одну СЕ +3. Запрет на включение детали в конкретную СЕ +4. Запрет на включение детали в любую СЕ +5. Числовые ограничения на СЕ, например, по массе, габаритам, составу и тд +Можно формализовать и структурные ограничения на гиперграф - возможность маскировки гиперребер – замены гиперребер на отдельные вершины в дереве сборки. Для этого маскируемые (схлопываемые) вершины должны принадлежать одной сборочной единице. + +Для оптимизации можно задать целевые функции, которые позволят формализовать принятие рациональных решений: +1. Большинство деталей должны войти в СЕ +2. Число СЕ должно быть максимальным +3. Механические связи высокой «валентности» целесообразно реализовывать на начальных этапах сборочного процесса. +4. Упрощение сборки сложного изделия путем минимизации числа механических связей на финальных операциях +5. Минимизировать число необходимых сопряжений для реализации механической связи. +При этом, в зависимости от специфики процесса, данный список можно дополнить требованиями и ограничениями, учитывающими специфику принятия решений. + +Данные принципы были реализованы в программном комплексе (далее - ПК) AssemBL, работающем в среде САПР Siemens NX 10.0. ( ["Структурный анализ изделия и проектирование сборочных комплексов в программном комплексе AssemBL"](https://cyberleninka.ru/article/n/strukturnyy-analiz-izdeliya-i-proektirovanie-sborochnyh-protsessov-v-programmnom-komplekse-assembl)) + +В данный комплекс входят подпрограммы, позволяющие осуществлять: +- Моделирование механических структур +- Структурный анализ конструкции +- Анализ геометрической разрешимости +- Синтез последовательности сборки +- Синтез декомпозиции изделия на сборочные единицы + +При этом, данный ПК опирается на ресурсы NX, в частности – команды меню Assemblies (Сборки) и Analysis (Анализ), а так же – на штатные инструменты NX для создания, редактирования и визуализации трехмерных моделей деталей и сборок. + +Сперва модуль анализирует модель, фиксирует существование механической связи между деталями. При этом, важно определить важные исключения – интерференции в сборке, зазоры, применение косвенного базирования, ограничения, введенные для моделирования законов движения в изделии. Определив их, оператор ПК должен штатными средствами NX устранить обнаруженные проблемы. + +Получив список механических связей, оператор выполняет экспертную постобработку, убирая ненужные для работы сопряжения и добавляя пары элементов, в каких применено косвенное базирование. Обработав и верифицировав эту информацию, возможно построить граф механических связей. При этом, программа анализирует построенный граф, вычленяет в его структуре клики. + +Далее, эксперт анализирует граф, выбирает те клики, которые представляют минимальный геометрически определенный фрагмент конструкции. Это позволяет перейти к построению гиперграфа. Полученный гиперграф в автоматическом режиме анализируется согласно изложенным выше принципам, производится проверка на стягиваемость, линеаризация графа (удаление избыточных связей). Создается s-гиперграф, позволяющий создать максимально большое число СЕ и последовательностей сборки. + +![Линеаризация и стягивание гиперграфа](img/HypergraphLinearisation.png) + +Линеаризация и стягивание гиперграфа + +Наконец, в автоматическом режиме или с помощью эксперта производится анализ геометрической разрешимости сборки. Анализ производится на основании отсутствия коллизий посредством инструментария NX. При этом, автор отмечает, что автоматический анализ даже для относительно несложных изделий достаточно ресурсоемкий и занимает много времени. + +Наконец, на основе всех полученных данных возможно произвести синтез последовательности сборки и разбиение изделия на сборочные единицы. + + + + ### 3D Model-Based Assembly Sequence Optimization using Insertionable Properties of Parts - 2020 Kento Tariki, Takuya Kiyokawa, Gustavo Alfonso Garcia Ricardez, Jun Takamatsu, Tsukasa Ogasawara (Japan) diff --git a/docs/technologies/img/AsmHypergraph.png b/docs/technologies/img/AsmHypergraph.png new file mode 100644 index 0000000000000000000000000000000000000000..58e2f56c68e3cab60b877bd3b94fd00ac63a05f6 GIT binary patch literal 55065 zcmeAS@N?(olHy`uVBq!ia0y~yU@Bu^U<~JAV_;y=_hJ6dz`(#*9OUlAuNSs54@I14-?iy0XB4ude`@%$Aj3=9m3nIRD+!FiblzNsaNDTyVC z3?NXgl$?`U5RjjlS5mBG6MS~|nsnNB+upaeb2gv<`G2qc{*Tt1Z$`b|{qFwGYvna@ z>wiXNpEZ4MJpZ-C{PdoWHlOwW-;WPa73y?Rn&_dDCRe}tk?}+i6%gO>u}9K$C{vwG 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