Existing model-based collision detection methods rely on accurate torque dynamic parameters identified using measured joint torques. However, for robots lacking joint torque sensors, only joint currents can be measured, and joint torques must be estimated through the linear relationship between joint currents and joint torque constants. This way can lead to cumulative identification errors in torque dynamic parameters, thereby diminishing the performance of model-based collision detection algorithms. To tackle this challenge, this article proposes an innovative collision detection method based on current residuals, which represent the disparities between measured joint currents and predicted joint currents computed by current dynamic parameters. Then, a dynamic threshold method for current residuals is designed to mitigate the impact of modeling errors at zero-speed direction changes on collision detection performance. Additionally, a suppression strategy based on online load identification and compensation is introduced to reduce the interference of non-collision load factors on collision detection signals. The proposed method mitigates the accumulation of errors on torque dynamic identification resulting from inaccuracies in joint torque constants, ultimately enhancing collision detection performance for robots without joint torque sensors. Extensive experiment results validate the correctness and effectiveness of this approach.