Industrial robots (IRs) have considerable energy-saving potential due to their vast application scale and wide range of applications. Although substantial work on the energy consumption (EC) optimization of IRs has emerged, most optimization approaches require prior knowledge of the IRs' dynamic characteristics and the electro-mechanical parameters of their drive systems, which are typically not provided by IR manufacturers. Therefore, this article proposes an EC modeling and optimization method based on the time-scaling technique and custom identification experimental data without joint torque information. Specifically, this article develops an energy characteristic parameter submodel (ECPSM) to formulate the EC resulting from configuration transitions. In addition, theoretical proof demonstrates that all coefficients in the proposed ECPSM can be identified based on the data of a finite number of identification experiments. Building upon the proposed EC model, a bidirectional dynamic programming (BDP) algorithm optimizes the IR's trajectory for energy-saving, while utilizing parallel processing significantly reduces the time required for the optimization process. Experimental results on the KUKA KR60-3 demonstrate that the proposed method achieves an average relative error of 1.59% for predicting the EC of linear scaling trajectories and 6.19% for nonlinear scaled trajectories. Moreover, the BDP-based optimization method dramatically reduces the computational time required to obtain the optimal scaling trajectory and its EC.