During pressure support ventilation, every breath is triggered by the patient. Mismatches between the patient and the ventilator are called asynchronies. It has been reported that large numbers of asynchronies may be harmful and may lead to increased mortality. Automatic asynchrony detection and classification, with subsequent feedback to clinicians, will improve lung ventilation and, possibly, patient outcome. Machine learning techniques have been used to detect asynchronies. However, large, diverse and high-quality training and verification data sets are needed. In this work, we propose a model for generating a large, realistic, labeled, synthetic dataset for training and testing machine learning algorithms to detect a wide variety of asynchrony types. Next to a morphological evaluation of the obtained waveforms, validation of the proposed model includes a test with a machine learning algorithm trained on clinical data.