Arabian Journal for Science and Engineering https://doi.org/10.1007/s13369-020-05094-1 RESEARCH ARTICLE-MECHANICAL ENGINEERING Optimization of Design Parameters Affecting the Performance of a Magnetic Fluid Rotary Seal Saurabh Parmar 1,2 · R. V. Upadhyay 1,2 · Kinnari Parekh 1,2 Received: 20 May 2020 / Accepted: 31 October 2020 © King Fahd University of Petroleum & Minerals 2020 Abstract Three different design parameters of magnetic fluid seal are optimized for the maximum pressure differential capacity of the seal. The program finite element method magnetics (FEMM) based on finite element method is used to find the magnetic flux inside the gap for all the combinations of the design parameters. The data are analyzed using the MINITAB statistical analysis software. The multivariable regression analysis technique is used to find the percentage effect of different parameters and also the optimized dimensions. The effect of magnetic fluid volume on maximum pressure differential capacity of a seal is observed, and the optimized volume is found. The results provide enough data to design and fabricate the seal. This seal can be used in positive as well as negative pressure applications. For example, as vacuum rotary shaft seal in low-pressure chemical vapor deposition machines, pressure seal for stirrer shaft in chemical process chambers to seal toxic gases. This seal can also be used as an exclusion seal, such as a bearing protection seals in robotic arms used in manufacturing plants. Keywords FEA · Magnetic fluid · Optimization · Regression analysis · Rotary seal 1 Introduction Magnetic fluid (also known as ferrofluid) is a colloidal sus- pension of magnetic nanoparticles suspended in carrier liquid [1]. The advantage of using the magnetic fluid is that it can be controlled by the external magnetic field [2]. The num- ber of biomedical [3–6] and technical applications [7–14] is developed using the magnetic fluid. The most successful technological application of magnetic fluid is magnetic fluid- based rotary shaft seal. In magnetic fluid shaft seal, the magnetic field holds the magnetic fluid into the clearance between the rotating shaft and stationary elements [15]. The important part of the mag- netic fluid seal is magnetic focusing structure. A simple magnetic focusing structure contains a permanent magnet, two magnetically soft pole-pieces and a shaft. The shaft can be either magnetic or non-magnetic. Non-magnetic shaft can B Saurabh Parmar 15drnst002@charusat.edu.in 1 Dr.K.C Patel R & D Centre, Charotar University of Science and Technology, Changa, Anand, Gujarat 388421, India 2 P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa, Anand, Gujarat 388421, India be used with the magnetic sleeve onto the shaft [16]. The magnetic flux is generated by the permanent magnet and focused into the annular gap using the two pole-pieces as shown in Fig. 1. The magnetic liquid introduced inside the annular gap is attracted by the intense magnetic field and makes the shape of an O-ring around the shaft. Thus, the gaps are sealed hermetically using the magnetic fluid. When the shaft rotates, the magnetic fluid adheres to the pole-piece and shaft. This ‘liquid O-ring’ is sheared between shaft and pole-pieces but remains in place to form a dynamic rotary seal. The magnetic field intensity is usually high at the gap, and therefore, the fluid magnetization reaches to its satura- tion value. The burst pressure P of a magnetic fluid seal is calculated from the formula [17],  P  N μ 0 M s ( B max − B min ) (1) where N is number of stages, μ 0  4π × 10 −7 N/A 2 is the permeability of space, and it can be determined using the experiment described in [18]. M s is saturation magnetization of magnetic fluid, and B max and B min are the maximum and minimum flux density, respectively, in the magnetic fluid. For single-stage seal, N  1. That means the magnetic fluid is introduced at only one annular gap. Figure 1 shows a schematic of two-stage seal. For the stages more than two, 123