{"id":15764,"date":"2018-08-30T15:41:50","date_gmt":"2018-08-30T15:41:50","guid":{"rendered":"https:\/\/www.simscale.com\/?page_id=15764"},"modified":"2023-07-24T12:05:05","modified_gmt":"2023-07-24T12:05:05","slug":"carbomech","status":"publish","type":"page","link":"https:\/\/www.simscale.com\/customers\/carbomech\/","title":{"rendered":"Carbomech\u00a0used SimScale FEA to develop a high-speed motorized spindle"},"content":{"rendered":"<div class=\"header-7-wrapper\" >    <div class=\"header-7-inner\">        <img decoding=\"async\" class=\"hw-section__image-background\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/08\/Carbomech-background.jpg\">        <div class=\"container\">            <div class=\"row\">                <div class=\"col-md-12\">                    <h1><strong>Carbomech<\/strong> used SimScale FEA to develop a high-speed motorized spindle<\/h1>                <\/div>            <\/div>            <div class=\"row\">                <div class=\"col-md-12\">                    <div class=\"header-widgets-wrapper\">                        <div class=\"header-widget\">                            <img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/03\/1-hour.png\" alt=\"From CAD to results in less than 1 hour\"\/>                            <p><strong>Time<\/strong> from CAD to results<\/p>                        <\/div>                    <\/div>                <\/div>            <\/div>        <\/div>    <\/div><\/div>\n\n\n<section class=\"about-customer-section\">    <div class=\"container\">        <div class=\"row\">            <div class=\"col-md-12\">                <div class=\"about-customer-section-inner\">                    <div class=\"customer-logo-wrapper\">                        <img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/08\/Carbomech-logo-260-x-116.png\" alt=\"\"\/>                    <\/div>                    <div class=\"customer-description-wrapper\">                        <p><\/p>                    <\/div>                <\/div>            <\/div>        <\/div>    <\/div><\/section>\n\n\n\n<p class=\"wp-block-paragraph\"><section class=\"acticle-customer-section\">    <div class=\"container\">        <div class=\"row\">            <div class=\"col-md-12\">                <div class=\"article-custom-section-inner\"><br><div class=\"social-icons-widget\">    <div class=\"share-options\">        <a href=\"https:\/\/www.facebook.com\/sharer\/sharer.php?u=https%3A%2F%2Fwww.simscale.com%2Fcustomers%2Fcarbomech%2F\" target=\"_blank\" class=\"share-option facebook-share\" aria-label=\"share SimScale on Facebook\" rel=\"noopener\">            <i class=\"fab fa-facebook-f\" aria-hidden=\"true\"><\/i>        <\/a>        <a href=\"https:\/\/www.linkedin.com\/shareArticle?mini=true&url=https%3A%2F%2Fwww.simscale.com%2Fcustomers%2Fcarbomech%2F&title=Carbomech%C2%A0used+SimScale+FEA+to+develop+a+high-speed+motorized+spindle\" target=\"_blank\" class=\"share-option linkedin-share\" aria-label=\"share SimScale on Linkedin\" rel=\"noopener\">            <i class=\"fab fa-linkedin-in\" aria-hidden=\"true\"><\/i>        <\/a>        <a href=\"https:\/\/twitter.com\/intent\/tweet?url=https%3A%2F%2Fwww.simscale.com%2Fcustomers%2Fcarbomech%2F&text=Carbomech%C2%A0used+SimScale+FEA+to+develop+a+high-speed+motorized+spindle\" target=\"_blank\" class=\"share-option twitter-share\" aria-label=\"share SimScale on Twitter\" rel=\"noopener\">            <span class=\"custom-x-icon\" aria-hidden=\"true\"><\/span>        <\/a>    <\/div><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">The Challenge<\/h4>\n\n\n\n<h2 class=\"wp-block-heading\">Find Natural Frequencies of a High-Speed Spindle Shaft and Dimension It with Strength Analysis<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Carbomech wanted to bring to the market a new air bearing spindle equipped with a DC motor which would be able to reach 180,000 rpm during operation. Finite element analysis (FEA) was used throughout the design phase to find the natural frequencies and modes of this design proposal and at the same time to dimension its geometry to guarantee that, when achieving high speeds, the deformation of the shaft\u2019s shape wouldn\u2019t generate issues with the air bearings.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/08\/Carbomech-spindle.png\" alt=\"spindle developed by Carbomech and optimized with SimScale\"\/><figcaption class=\"wp-element-caption\">CM180 spindle developed by Carbomech and optimized with SimScale<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Being a startup, Carbomech could not afford to test all the design proposals they had. Consequently, adding numerical simulations early in the design phase of this new spindle was the right solution to save time and money while knowing that the results were accurate.<\/p>\n\n\n                <\/div>            <\/div>        <\/div>    <\/div><\/section>\n\n\n<section class=\"testimonial3-section\">    <div class=\"testimonial-icon\"><\/div>    <div class=\"container\">        <div class=\"row\">            <div class=\"col-md-12\">                <p class=\"testimonial-text\">A big part of the experience with SimScale is the support. Even if SimScale gets better and better, there are so many choices. You must have somebody helping you to choose!<\/p>            <\/div>        <\/div>        <div class=\"row\">            <div class=\"col-md-12\">                <div class=\"testimonial-bottom\">                    <div class=\"testimonial-image-wrapper\">                        <img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/08\/Fabrizio-Pauri-131-x-131.png\" alt=\"\"\/>                    <\/div>                    <div class=\"testimonial-info-wrapper\">                        <p class=\"name\">Fabrizio Pauri<\/p>                        <p class=\"title\">CEO and Chief Engineer, Carbomech<\/p>                    <\/div>                <\/div>            <\/div>        <\/div>    <\/div><\/section>\n\n\n<section class=\"acticle-customer-section\">    <div class=\"container\">        <div class=\"row\">            <div class=\"col-md-12\">                <div class=\"article-custom-section-inner\">\n\n\n\n<h4 class=\"wp-block-heading\">How they solved it with SimScale<\/h4>\n\n\n\n<h2 class=\"wp-block-heading\">Finding Natural Frequencies and Elastic Deformation Due to the Shaft&#8217;s Rotational Speed<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The project involved running a modal analysis to find the right compromise between stiffness and mass. The aim was to operate the shaft at speeds safely distant from the natural frequencies where spindle destruction is certain.<\/p>\n\n\n\n<figure class=\"wp-block-video\"><video height=\"1080\" style=\"aspect-ratio: 1920 \/ 1080;\" width=\"1920\" autoplay loop muted preload=\"none\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/02\/MODE7.mp4\" playsinline><\/video><figcaption class=\"wp-element-caption\">First natural mode: bending<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">After achieving a desired configuration based on the natural modes and frequencies, Carbomech\u2019s CEO and Chief Engineer Fabrizio Pauri also ran a centrifugal load analysis of the shaft to check stresses and deformation on the spindle at 180,000 rpm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The spindles measure around 0.13m in length and have different cross sections with the outer diameter varying from 6mm to 20mm. In order to properly assess this kind of geometries, a second order element mesh was created with around 500 thousand elements.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/08\/Carbomech-spindle-mesh.png\" alt=\"second order element mesh used for modal and strength analysis of a spindle by Carbomech with SimScale\"\/><figcaption class=\"wp-element-caption\">Second order element mesh used for modal and strength analysis<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A modal analysis was then performed for two different spindle designs as part of the first stage in the development phase. The main goal was to assess the natural frequencies and modes of the spindles in order to check if changes in terms of mass distribution would be needed to guarantee a good stiffness.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Finding the natural frequencies helped to define the speed range where the shaft can run safely.<\/p>\n\n\n\n<figure class=\"wp-block-video\"><video height=\"1080\" style=\"aspect-ratio: 1920 \/ 1080;\" width=\"1920\" autoplay loop muted preload=\"none\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/02\/MODE8.mp4\" playsinline><\/video><figcaption class=\"wp-element-caption\">Second natural mode: radial expansion<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Operating the spindle too near to a natural frequency would deform the shaft in such a way that it will crash against the surfaces of the air bearings.<\/p>\n\n\n\n<figure class=\"wp-block-video\"><video height=\"1080\" style=\"aspect-ratio: 1920 \/ 1080;\" width=\"1920\" autoplay loop muted preload=\"none\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/02\/MODE9.mp4\" playsinline><\/video><figcaption class=\"wp-element-caption\">Third natural mode: rotation<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Following the design phase, a centrifugal load analysis was then performed by using the same second order element mesh which was previously created. Boundary conditions were then assigned to mimic the air bearing case and a centrifugal load of 180,000 rpm was applied to the spindle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">With this kind of analysis, the main goal was to assess the displacement around the \u2018disk\u2019 which stays inside the bearing\u2019s case and has limited space to expand due to a high rotational speed. The stresses were also assessed with the online post-processor tool available inside SimScale.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/08\/Carbomech-simulations.png\" alt=\"stress distribution for original and deformed shape of a spindle, FEA in the web browser with SimScale\"\/><figcaption class=\"wp-element-caption\">Stress distribution for the original and deformed shape<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">                <\/div>            <\/div>        <\/div>    <\/div><\/section><br><section class=\"acticle-customer-section\">    <div class=\"container\">        <div class=\"row\">            <div class=\"col-md-12\">                <div class=\"article-custom-section-inner\">\n\n\n\n<h4 class=\"wp-block-heading\">The results<\/h4>\n\n\n\n<h2 class=\"wp-block-heading\">Calculating Displacement and Reducing Physical Prototypes by 50%<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Since the gap between parts in relative movement is in the range of few micrometers where air bearings are used, it is crucial to correctly simulate all the deformations of the shaft.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/08\/Carbomech-simulation-displacement-distribution.png\" alt=\"Displacement distribution for the original and deformed shape, FEA of a spindle by Carbomech with SimScale\"\/><figcaption class=\"wp-element-caption\">Displacement distribution for the original and deformed shape<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">With the use of FEA with the SimScale cloud-based platform, the Carbomech team could then calculate the displacement due to the high speed of the spindle on this region of interest, at 180,000 rotations per minute.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u201cSupport is super good! The few times I had something wrong or hadn\u2019t understood something, I would simply email the Customer Success Engineer and minutes later the solution was there. I can only say that the level of support is very good!\u201d<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">The FEA simulations performed in the cloud with SimScale gave Carbomech\u2019s team valuable insights into the mechanical performance of their high-speed spindle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The team had to build 50% less prototypes for physical testing than usual by adding SimScale to the design phase. The price of each spindle is 3-4 times more than a SimScale subscription, which makes the return on investment (ROI) very high.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">                <\/div>            <\/div>        <\/div>    <\/div><\/section><br><section class=\"acticle-customer-section\">    <div class=\"container\">        <div class=\"row\">            <div class=\"col-md-12\">                <div class=\"article-custom-section-inner\">\n\n\n\n<h4 class=\"wp-block-heading\">Next Steps<\/h4>\n\n\n\n<h2 class=\"wp-block-heading\">Continuing to Use SimScale to Finalize the Current Project and Future Ones<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/08\/Carbomech-team-1.jpg\" alt=\"Carbomech team: Fabrizio Pauri, Fabrizio Pejla, Alex Vallino (from the left)\"\/><figcaption class=\"wp-element-caption\">Carbomech team: Fabrizio Pauri, Fabrizio Pejla, Alex Vallino (from the left)<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The current CM180 spindle has been redesigned by using the results from simulations made with SimScale. An improved design has already been validated by further simulations with the platform and is currently in development.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u201cWell, I have a dedicated Customer Success Engineer watching over me, helping me to actually squeeze out the value from the service. What more can I ask for?\u201d<\/p>\n<\/blockquote>\n\n\n\n<div class=\"hw-acticleFooter \">\n    <p>Set up your own cloud-native simulation via the web in minutes by creating an account on the SimScale platform. No installation, special hardware or credit card is required.<\/p>\n    <div class=\"hw-acticleFooter__buttons\">\n                    <a class=\"btn2 btn2-primary\" href=\"https:\/\/www.simscale.com\/signup\/\" >Start Simulating<\/a>\n                            <a class=\"btn2 btn2-default\" href=\"https:\/\/www.simscale.com\/product\/pricing\/#demo\" >Request Demo<\/a><\/div>\n        <\/div>\n\n\n\n                <\/div>            <\/div>        <\/div>    <\/div><\/section>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n\n<div   class=\"hw-section hw-section--normalSpacing hw-section--white\">\n\n        <div class=\"hw-contentWrap hw-contentWrap--normalWidth hw-textLeft\">\n        \n        \n\n\n<h2 class=\"wp-block-heading has-text-align-center\">See More Success Stories<\/h2>\n\n\n<div class=\"hw-grid hw-grid--cards\">\n    \n\n        <div class=\"hw-card\" data-type=\"architecture-engineering-&amp;-construction-(AEC)\" data-title=\"Johnson Screens\u00a0used SimScale CFD to verify airflow through their architectural radiator grille product\">\n\n            <a class=\"hw-card__top\" href=\"https:\/\/www.simscale.com\/customers\/johnson-screens\/\">\n\n                            <img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"169\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/03\/sliceGrill-v2-300x169.png\" class=\"hw-card__topImage\" alt=\"Velocity profile of a typical section of a grille.\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/03\/sliceGrill-v2-300x169.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2018\/03\/sliceGrill-v2-e1521655078616.png 768w, https:\/\/frontend-assets.simscale.com\/media\/2018\/03\/sliceGrill-v2-1024x576.png 1024w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>    \n                                    <h4 class=\"hw-card__topTitle\">Johnson Screens\u00a0used SimScale CFD to verify airflow through their architectural radiator grille product<\/h4>\n                \n            <\/a>\n\n            \n                <div class=\"hw-card__body\">\n\n                                <img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"114\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/07\/johnson_screens_logo_small.svg\" class=\"hw-card__logo\" alt=\"\" \/>    \n                    <div class=\"hw-card__categories\"><span class=\"hw-category-item\" data-type=\"architecture-engineering-&#038;-construction-(AEC)\">AEC<\/span><\/div>\n                <\/div>\n\n            \n        <\/div>\n\n\n        <div class=\"hw-card\" data-type=\"machinery-&amp;-industrial-equipment\" data-title=\"Furnace Fixers\u00a0used CFD with SimScale to improve the performance of its furnace by 40%\">\n\n            <a class=\"hw-card__top\" href=\"https:\/\/www.simscale.com\/customers\/furnace-fixers\/\">\n\n                            <img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"129\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/02\/Furnace-Fixers-case-study-300x129.jpg\" class=\"hw-card__topImage\" alt=\"Furnace Fixers case study\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2018\/02\/Furnace-Fixers-case-study-300x129.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2018\/02\/Furnace-Fixers-case-study-768x329.jpg 768w, https:\/\/frontend-assets.simscale.com\/media\/2018\/02\/Furnace-Fixers-case-study-1024x439.jpg 1024w, https:\/\/frontend-assets.simscale.com\/media\/2018\/02\/Furnace-Fixers-case-study.jpg 1600w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>    \n                                    <h4 class=\"hw-card__topTitle\">Furnace Fixers\u00a0used CFD with SimScale to improve the performance of its furnace by 40%<\/h4>\n                \n            <\/a>\n\n            \n                <div class=\"hw-card__body\">\n\n                                <img loading=\"lazy\" decoding=\"async\" width=\"185\" height=\"100\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/07\/furnace_fixers_logo_small.png\" class=\"hw-card__logo\" alt=\"\" \/>    \n                    <div class=\"hw-card__categories\"><span class=\"hw-category-item\" data-type=\"machinery-&#038;-industrial-equipment\">Machinery &#038; Industrial Equipment<\/span><\/div>\n                <\/div>\n\n            \n        <\/div>\n\n\n        <div class=\"hw-card\" data-type=\"machinery-&amp;-industrial-equipment\" data-title=\"Anderson CNC\u00a0found the perfect smoke outlets location for a CNC plasma table with SimScale\">\n\n            <a class=\"hw-card__top\" href=\"https:\/\/www.simscale.com\/customers\/anderson-cnc\/\">\n\n                            <img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"124\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2017\/12\/Anderson-simulation-results2-300x124.png\" class=\"hw-card__topImage\" alt=\"Anderson plasma tabe\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2017\/12\/Anderson-simulation-results2-300x124.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2017\/12\/Anderson-simulation-results2-768x318.png 768w, https:\/\/frontend-assets.simscale.com\/media\/2017\/12\/Anderson-simulation-results2-1024x425.png 1024w, https:\/\/frontend-assets.simscale.com\/media\/2017\/12\/Anderson-simulation-results2.png 1500w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>    \n                                    <h4 class=\"hw-card__topTitle\">Anderson CNC\u00a0found the perfect smoke outlets location for a CNC plasma table with SimScale<\/h4>\n                \n            <\/a>\n\n            \n                <div class=\"hw-card__body\">\n\n                                <img loading=\"lazy\" decoding=\"async\" width=\"266\" height=\"100\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/07\/stryker_machines_logo_small.png\" class=\"hw-card__logo\" alt=\"stryker machines logo\" \/>    \n                    <div class=\"hw-card__categories\"><span class=\"hw-category-item\" data-type=\"machinery-&#038;-industrial-equipment\">Machinery &#038; Industrial Equipment<\/span><\/div>\n                <\/div>\n\n            \n        <\/div>\n\n\n\n<\/div>\n\n\n<div class=\"hw-block hw-btnWrapper hw-btnWrapper--alignCenter \">\n    <a href=\"\/customers\/\" class=\"hw-btn  hw-btn--secondary  \"     >\n        See All Success Stories    <\/a>\n<\/div>\n\n\n\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n<section class=\"customer-bottom-bar\">    <img decoding=\"async\" loading=\"lazy\" class=\"hw-section__image-background\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2019\/12\/enterprise_header.png\">    <div class=\"container\">        <div class=\"row\">            <div class=\"col-md-12\">                <h2>Have you considered the potential a cloud-native simulation platform could bring to your organization? Learn about SimScale<\/h2>            <\/div>        <\/div>        <div class=\"row\">            <div class=\"col-md-12 text-center\">                <a href=\"https:\/\/www.simscale.com\/cloud-solution\/\" class=\"btn2 btn2-default\">Find Out More<\/a>            <\/div>        <\/div>    <\/div><\/section>\n","protected":false},"excerpt":{"rendered":"<p>The Challenge Find Natural Frequencies of a High-Speed Spindle Shaft and Dimension It with Strength Analysis Carbomech wanted...","protected":false},"author":4,"featured_media":15778,"parent":8006,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/template-individual-customer-page2.php","meta":{"_acf_changed":false,"_crdt_document":"","inline_featured_image":false,"footnotes":""},"class_list":["post-15764","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/15764","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/comments?post=15764"}],"version-history":[{"count":0,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/15764\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/8006"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media\/15778"}],"wp:attachment":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media?parent=15764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}