Proceedings of the Seminar on Molds, Dies and Tools


ISSN 5463-5463

Title

INSERÇÃO DA INTERPOLAÇÃO SPLINE NA MANUFATURA DE SUPERFÍCIES COMPLEXAS

INSERTION OF SPLINE INTERPOLATION IN THE MANUFACTURE OF COMPLEX SURFACES

DOI

10.5151/5463-5463-17071

Downloads

186 Downloads

Abstract

Atualmente a globalização vem refletindo em um aumento exponencial de competitividade em todos os ramos de mercados, o que resulta para as empresas um investimento na direção de melhoria da qualidade do produto, reduções de custos e tempo de fabricação. Estudos recentes mostram que o processo de usinagem de superfícies complexas atual, através da trajetória da ferramenta sendo representada por Interpolação Linear, está cada vez mais defasado quando se comparado com a Interpolação Spline, uma vez que a Interpolação Linear se torna inviável no representação de superfícies complexas devido à dificuldade de se manter a geometria da peça respeitando os limites de tolerâncias, exatidão geométrica e tempo de usinagem. Como sabe-se, Interpolação Linear é a trajetória da ferramenta baseada em segmentos de retas, já na Interpolação Spline a trajetória da ferramenta é representada por um modelo matemático capaz de gerar trajetória de uma superfície complexa através de segmentos de curvas. Utilizando o Sistema CAM para representar a trajetória da ferramenta, observa-se que além das tolerâncias que o próprio Sistema CAM necessita, uma nova tolerância, chamada tolerância NURBS, é necessária quando se usa Interpolação Spline. Em virtude disto, este artigo visou conhecer e compreender este método de Interpolação, analisando as influências desta tolerância Spline e integrá-lo como auxilio na indústria de moldes e matrizes. Para atingir esses objetivos, foi utilizado um corpo de prova cuja as características superficiais se assemelham ao utilizado em industrias de moldes e matrizes. Posteriormente, foi feito a comparação do tempo de usinagem fornecido pelo Sistema CAM com o tempo real, a comparação da rugosidade superficial e a exatidão geométrica.

 

Currently, due to technological advance, the competition for the consumer market and territory in the manufacturing sector, is growing increasingly. Considering this, companies are investing very high on the issue of better product quality, low price and delivery time. With this growing companies are searching alternatives to improve the process of manufacturing its products. Because of this, recent studies show that the current method of machining by Linear Interpolation, is increasingly out of step when compared with Spline Interpolation. As is known, Linear Interpolation is the trajectory of the tool based on straight line segments, as Spline Interpolation is a mathematical model capable of generating complex trajectory of a complex surface by segments of curves. Using the CAM system as a tool for process simulation, we see that beyond the tolerances CAM system itself needs a new tolerance, called NURBS tolerance is needed when using Spline interpolation. Because of this, this project looks to know and understand this new method of interpolation, analyzing the influences of tolerance NURBS and integrate it as an aid in the manufacture of molds and dies. To achieve these objectives, we used a specimen whose surface characteristics are similar to that used in industrial molds and dies, and this was done with the machining of this specimen. Later, he was made to compare the machining time provided by the CAM system with real time, the comparison of surface roughness and geometric accuracy. Finally, taking into account the need of industries to accelerate the production process without letting quality fall, this project develops a method rarely used, improving it and integrating it in the string CAD / CAM / CNC.

Keywords

Interpolação Spline; Superfícies complexas.

Spline interpolation; Surface complex.

How to refer

Priore, Marco Aurélio Garrido; Helleno, André Luís; Monaro, Renato Luis Garrido. INSERÇÃO DA INTERPOLAÇÃO SPLINE NA MANUFATURA DE SUPERFÍCIES COMPLEXAS , p. 41-49. In: 8º Encontro de Cadeia de Ferramentas, Moldes e Matrizes, São Paulo, 2010.
ISSN: 5463-5463 , DOI 10.5151/5463-5463-17071

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(1/1) ErrorException

fwrite(): write of 1826 bytes failed with errno=28 No space left on device

in StreamHandler.php line 131
at HandleExceptions->handleError(8, 'fwrite(): write of 1826 bytes failed with errno=28 No space left on device', '/var/www/webroot/ROOT/vendor/monolog/monolog/src/Monolog/Handler/StreamHandler.php', 131, array('stream' => resource, 'record' => array('message' => 'file_put_contents(): write of 325 bytes failed with errno=28 No space left on device', 'context' => array('exception' => object(ErrorException)), 'level' => 400, 'level_name' => 'ERROR', 'channel' => 'production', 'datetime' => object(DateTime), 'extra' => array(), 'formatted' => '[2025-05-31 19:37:47] production.ERROR: file_put_contents(): write of 325 bytes failed with errno=28 No space left on device {"exception":"[object] (ErrorException(code: 0): file_put_contents(): write of 325 bytes failed with errno=28 No space left on device at /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:122)[stacktrace]#0 [internal function]: Illuminate\\\\Foundation\\\\Bootstrap\\\\HandleExceptions->handleError(8, \'file_put_conten...\', \'/var/www/webroo...\', 122, Array)#1 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php(122): file_put_contents(\'/var/www/webroo...\', \'a:5:{s:6:\\"_toke...\', 2)#2 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/FileSessionHandler.php(83): Illuminate\\\\Filesystem\\\\Filesystem->put(\'/var/www/webroo...\', \'a:5:{s:6:\\"_toke...\', true)#3 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/Store.php(128): Illuminate\\\\Session\\\\FileSessionHandler->write(\'vKy41XX8JLepLHY...\', \'a:5:{s:6:\\"_toke...\')#4 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/Middleware/StartSession.php(87): Illuminate\\\\Session\\\\Store->save()#5 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Foundation/Http/Kernel.php(218): Illuminate\\\\Session\\\\Middleware\\\\StartSession->terminate(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#6 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Foundation/Http/Kernel.php(189): Illuminate\\\\Foundation\\\\Http\\\\Kernel->terminateMiddleware(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#7 /var/www/webroot/ROOT/public/index.php(59): Illuminate\\\\Foundation\\\\Http\\\\Kernel->terminate(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#8 {main}"} ')))
at fwrite(resource, '[2025-05-31 19:37:47] production.ERROR: file_put_contents(): write of 325 bytes failed with errno=28 No space left on device {"exception":"[object] (ErrorException(code: 0): file_put_contents(): write of 325 bytes failed with errno=28 No space left on device at /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:122)[stacktrace]#0 [internal function]: Illuminate\\\\Foundation\\\\Bootstrap\\\\HandleExceptions->handleError(8, \'file_put_conten...\', \'/var/www/webroo...\', 122, Array)#1 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php(122): file_put_contents(\'/var/www/webroo...\', \'a:5:{s:6:\\"_toke...\', 2)#2 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/FileSessionHandler.php(83): Illuminate\\\\Filesystem\\\\Filesystem->put(\'/var/www/webroo...\', \'a:5:{s:6:\\"_toke...\', true)#3 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/Store.php(128): Illuminate\\\\Session\\\\FileSessionHandler->write(\'vKy41XX8JLepLHY...\', \'a:5:{s:6:\\"_toke...\')#4 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/Middleware/StartSession.php(87): Illuminate\\\\Session\\\\Store->save()#5 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Foundation/Http/Kernel.php(218): Illuminate\\\\Session\\\\Middleware\\\\StartSession->terminate(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#6 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Foundation/Http/Kernel.php(189): Illuminate\\\\Foundation\\\\Http\\\\Kernel->terminateMiddleware(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#7 /var/www/webroot/ROOT/public/index.php(59): Illuminate\\\\Foundation\\\\Http\\\\Kernel->terminate(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#8 {main}"} ')in StreamHandler.php line 131
at StreamHandler->streamWrite(resource, array('message' => 'file_put_contents(): write of 325 bytes failed with errno=28 No space left on device', 'context' => array('exception' => object(ErrorException)), 'level' => 400, 'level_name' => 'ERROR', 'channel' => 'production', 'datetime' => object(DateTime), 'extra' => array(), 'formatted' => '[2025-05-31 19:37:47] production.ERROR: file_put_contents(): write of 325 bytes failed with errno=28 No space left on device {"exception":"[object] (ErrorException(code: 0): file_put_contents(): write of 325 bytes failed with errno=28 No space left on device at /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:122)[stacktrace]#0 [internal function]: Illuminate\\\\Foundation\\\\Bootstrap\\\\HandleExceptions->handleError(8, \'file_put_conten...\', \'/var/www/webroo...\', 122, Array)#1 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php(122): file_put_contents(\'/var/www/webroo...\', \'a:5:{s:6:\\"_toke...\', 2)#2 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/FileSessionHandler.php(83): Illuminate\\\\Filesystem\\\\Filesystem->put(\'/var/www/webroo...\', \'a:5:{s:6:\\"_toke...\', true)#3 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/Store.php(128): Illuminate\\\\Session\\\\FileSessionHandler->write(\'vKy41XX8JLepLHY...\', \'a:5:{s:6:\\"_toke...\')#4 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/Middleware/StartSession.php(87): Illuminate\\\\Session\\\\Store->save()#5 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Foundation/Http/Kernel.php(218): Illuminate\\\\Session\\\\Middleware\\\\StartSession->terminate(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#6 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Foundation/Http/Kernel.php(189): Illuminate\\\\Foundation\\\\Http\\\\Kernel->terminateMiddleware(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#7 /var/www/webroot/ROOT/public/index.php(59): Illuminate\\\\Foundation\\\\Http\\\\Kernel->terminate(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#8 {main}"} '))in StreamHandler.php line 117
at StreamHandler->write(array('message' => 'file_put_contents(): write of 325 bytes failed with errno=28 No space left on device', 'context' => array('exception' => object(ErrorException)), 'level' => 400, 'level_name' => 'ERROR', 'channel' => 'production', 'datetime' => object(DateTime), 'extra' => array(), 'formatted' => '[2025-05-31 19:37:47] production.ERROR: file_put_contents(): write of 325 bytes failed with errno=28 No space left on device {"exception":"[object] (ErrorException(code: 0): file_put_contents(): write of 325 bytes failed with errno=28 No space left on device at /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:122)[stacktrace]#0 [internal function]: Illuminate\\\\Foundation\\\\Bootstrap\\\\HandleExceptions->handleError(8, \'file_put_conten...\', \'/var/www/webroo...\', 122, Array)#1 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php(122): file_put_contents(\'/var/www/webroo...\', \'a:5:{s:6:\\"_toke...\', 2)#2 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/FileSessionHandler.php(83): Illuminate\\\\Filesystem\\\\Filesystem->put(\'/var/www/webroo...\', \'a:5:{s:6:\\"_toke...\', true)#3 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/Store.php(128): Illuminate\\\\Session\\\\FileSessionHandler->write(\'vKy41XX8JLepLHY...\', \'a:5:{s:6:\\"_toke...\')#4 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/Middleware/StartSession.php(87): Illuminate\\\\Session\\\\Store->save()#5 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Foundation/Http/Kernel.php(218): Illuminate\\\\Session\\\\Middleware\\\\StartSession->terminate(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#6 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Foundation/Http/Kernel.php(189): Illuminate\\\\Foundation\\\\Http\\\\Kernel->terminateMiddleware(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#7 /var/www/webroot/ROOT/public/index.php(59): Illuminate\\\\Foundation\\\\Http\\\\Kernel->terminate(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#8 {main}"} '))in AbstractProcessingHandler.php line 39
at AbstractProcessingHandler->handle(array('message' => 'file_put_contents(): write of 325 bytes failed with errno=28 No space left on device', 'context' => array('exception' => object(ErrorException)), 'level' => 400, 'level_name' => 'ERROR', 'channel' => 'production', 'datetime' => object(DateTime), 'extra' => array(), 'formatted' => '[2025-05-31 19:37:47] production.ERROR: file_put_contents(): write of 325 bytes failed with errno=28 No space left on device {"exception":"[object] (ErrorException(code: 0): file_put_contents(): write of 325 bytes failed with errno=28 No space left on device at /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:122)[stacktrace]#0 [internal function]: Illuminate\\\\Foundation\\\\Bootstrap\\\\HandleExceptions->handleError(8, \'file_put_conten...\', \'/var/www/webroo...\', 122, Array)#1 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php(122): file_put_contents(\'/var/www/webroo...\', \'a:5:{s:6:\\"_toke...\', 2)#2 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/FileSessionHandler.php(83): Illuminate\\\\Filesystem\\\\Filesystem->put(\'/var/www/webroo...\', \'a:5:{s:6:\\"_toke...\', true)#3 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/Store.php(128): Illuminate\\\\Session\\\\FileSessionHandler->write(\'vKy41XX8JLepLHY...\', \'a:5:{s:6:\\"_toke...\')#4 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Session/Middleware/StartSession.php(87): Illuminate\\\\Session\\\\Store->save()#5 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Foundation/Http/Kernel.php(218): Illuminate\\\\Session\\\\Middleware\\\\StartSession->terminate(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#6 /var/www/webroot/ROOT/vendor/laravel/framework/src/Illuminate/Foundation/Http/Kernel.php(189): Illuminate\\\\Foundation\\\\Http\\\\Kernel->terminateMiddleware(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#7 /var/www/webroot/ROOT/public/index.php(59): Illuminate\\\\Foundation\\\\Http\\\\Kernel->terminate(Object(Illuminate\\\\Http\\\\Request), Object(Illuminate\\\\Http\\\\Response))#8 {main}"} '))in Logger.php line 344
at Logger->addRecord(400, 'file_put_contents(): write of 325 bytes failed with errno=28 No space left on device', array('exception' => object(ErrorException)))in Logger.php line 707
at Logger->error('file_put_contents(): write of 325 bytes failed with errno=28 No space left on device', array('exception' => object(ErrorException)))in Writer.php line 203
at Writer->writeLog('error', 'file_put_contents(): write of 325 bytes failed with errno=28 No space left on device', array('exception' => object(ErrorException)))in Writer.php line 114
at Writer->error('file_put_contents(): write of 325 bytes failed with errno=28 No space left on device', array('exception' => object(ErrorException)))in Handler.php line 113
at Handler->report(object(ErrorException))in Handler.php line 100
at Handler->report(object(ErrorException))in HandleExceptions.php line 81
at HandleExceptions->handleException(object(ErrorException))