We performed near-daily observations on the binary pulsars PSR J0218+4232, PSR J1518+4904 and PSR J2023+2853 with the Canadian Hydrogen Intensity Mapping Experiment (CHIME). For the first time, we detected the Shapiro time delay in all three pulsar-binary systems, using only 2--4 years of CHIME/Pulsar timing data. We measured the pulsar masses to be 1.49+0.23-0.20 M_, 1.470+0.030-0.034 M_ and 1.50+0.49-0.38 M_ respectively. The companion mass to PSR J0218+4232 was found to be 0.179+0.018-0.016 M_. We constrained the mass of the neutron-star companion of PSR J1518+4904 to be 1.248+0.035-0.029 M_, using the observed apsidal motion as a constraint on mass estimation. The binary companion to PSR J2023+2853 was found to have a mass of 0.93+0.17-0.14 M_; in the context of the near-circular orbit, this mass estimate suggests that the companion to PSR J2023+2853 is likely a high-mass white dwarf. By comparing the timing model obtained for PSR J0218+4232 with previous observations, we found a significant change in the observed orbital period of the system of Pb = 0.14(2) × 10⁻¹²; we determined that this variation arises from ``Shklovskii acceleration" due to relative motion of the binary system, and used this measurement to estimate a distance of d=(6.7 ± 1.0) kpc to PSR J0218+4232. This work demonstrates the capability of high-cadence observations, enabled by the CHIME/Pulsar system, to detect and refine general-relativistic effects of binary pulsars over short observing timescales.
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