Surface roughness is a key factor in different machining processes and plays an important role in ergonomics, assembly process, wear and fatigue life of components. Other factors like functionality, performance and durability of parts are also affected by surface roughness. Although maintaining an optimum surface roughness is a major challenge in many manufacturing industries. Surface roughness during machining depends upon machining parameters such as tool geometry, feed rate, depth of cut, rotational speed, lubrication, tool wear, etc. Tool vibrations during machining also have significant influence in surface roughness. In this work an attempt is made to predict the surface roughness of machined components made by the turning process by using machine learning of tool vibration signals. By varying different machining parameters and keeping other tooling and material properties same, a range of surface roughness values can be obtained. For each condition, corresponding tool vibration signals were recorded. Our experimental setup involves a vibration data collector which is used for recording vibration signals generated during the turning operation. The collected data preprocessed and categorized into training and test sets. Various machine learning regression techniques including Linear Regression, Ridge Regression, Support Vector Regression (SVR), Decision Tree Regression, Random Forest Regression, Gradient Boosting Regression, K-Nearest Neighbors Regression (KNN), and Neural Network Regression were used to predict the surface roughness. The study highlights the importance of feature extraction and model selection in achieving accurate and reliable surface roughness predictions, ultimately contributing to enhanced machining process control and product quality.