I see you try to set ylim but you give bad values. This will change the scale of the plot (like a zoom). For example see this:
par(mfrow=c(2,1))
tN <- table(Ni <- stats::rpois(100, lambda = 5))
r <- barplot(tN, col = rainbow(20),ylim=c(0,50),main='long y-axis')
r <- barplot(tN, col = rainbow(20),main='short y axis')
Another option is to plot without axes and set them manually using axis and usr:
require(grDevices) # for colours
par(mfrow=c(1,1))
r <- barplot(tN, col = rainbow(20),main='short y axis',ann=FALSE,axes=FALSE)
usr <- par("usr")
par(usr=c(usr[1:2], 0, 20))
axis(2,at=seq(0,20,5))
