Digital twins are revolutionizing smart manufacturing by facilitating real-time monitoring, simulation, and optimization of physical processes. This paper introduces the SINDIT framework, a comprehensive approach tailored for developing knowledge graph-based digital twins. By seamlessly integrating cognitive capabilities, SINDIT enhances decision-making and operational efficiency within manufacturing systems. Central to its architecture is a robust data pipeline, adept at organizing and linking vast amounts of heterogeneous data, thereby enabling advanced data analytics and reasoning. Case studies from the pilots of the COGNIMAN project underscore the practical utility and benefits of the SINDIT framework. These studies showcase notable enhancements in predictive maintenance, process optimization, and overall productivity. By harnessing the power of knowledge graphs and cognitive capabilities, SINDIT represents a promising avenue for driving innovation and efficiency in smart manufacturing. Through this framework, manufacturers can achieve a higher level of operational insight and agility, leading to improved performance and competitiveness in the market.