Force-balanced coil (FBC) is a helically wound hybrid coil of toroidal filed coils and a solenoid. The FBC can significantly reduce the required mass of the structure for induced electromagnetic forces. Based on the FBC design, a superconducting model coil using NbTi strands has been developed. The critical coil current and the critical magnetic filed in 4.2 K are 552 A and 7.1 T, respectively. The hand-made windings were neither impregnated with epoxy resin nor reinforced with stainless steel wires. Four test runs were conducted at intervals of several months with liquid helium cooling, including supercooled liquid helium based on the saturated vapor pressure. The model FBC maintained the training phenomena even after the coil was warmed up to room temperature. After 107 quenches the maximum quench current was 492 A, corresponding to 89% of the critical current, and it was successfully excited up to 6.3 T. In the third and fourth test runs, the quench properties were investigated using acoustic emission (AE) measurements. This study mainly contributes to estimating the relationship between the performance and the helical winding conditions of the model FBC based on the AE signals.