So pretty much lets just ignore the frequency from the micro-controller. It sounds like I have the math right for figuring out what torque I need to produce from the load end of things and now I just need to figure out what the motor can produce at various speeds. Looking at the datasheet for full stepping it shows 70.31% current through each phase. I'm assuming that the holding torque rating of a motor is the torque produced at the rated current through both phases. The lowest current is when it drives 100% current through only one phase when half stepping or micro stepping. Is my assumption about holding torque correct in regards to it requiring the rated current through both phases? If so then it appears that at most the torque would be 70.31% of the holding torque and as little as 50%.
Knowing the supply voltage and motor resistance and inductance I can find the time it takes to reach the current limit or I could determine what current I can achieve within a shorter time period at a reduced torque. When looking at the current table in the driver datasheet and it says the percentage of the trip current to each phase I'm understanding that to mean that the driver will apply the supply voltage until the target current percentage is reached or as close to it as it can get if the on time is too short. For example under 1/16th stepping it shows 100% on phase 1 for step 1 and 2, then 98.44%, 95.31%, 92.19%. If the on time isn't long enough to reach 100% on step one then the current just looks like the exponential increasing curve. Then there would be some slow decay because the next step is increasing but on step 2 the current is already at some percentage of the trip current so it continues to try and reach it's target percentage.
I've taken the data from the current table and plotted the points which resemble sine and cosine waves but mathematically they don't match so I'm not sure how the manufacturer came up with those specific current percentage values. I also tried computing the values from a sine and cosine function and then computed their values +/- 5% which is the deviance given in the spec sheet. The values fall within those ranges from the real sine and cosine functions but with no specific pattern. I also noticed that when I did a regression fit to the datasheet values, a 6th order polynomial fit almost perfectly, much better than sine or cosine so I'm thinking that maybe they used a polynomial approximation because it is easier to calculate than sine and cosine.
I guess part of what's not making sense with this is that the net torque varies quite a bit in between full steps which I would have expected the phase currents to produce a relatively constant net torque but vary the ratio between the 2 phases. If at each full step each phase is run at 70.31% of the trip current then why do the micro steps not also average 70.31% over the 2 phases? Obviously if a phase can only go to 100% of it's trip current and each phase cycles between 0-100% then the most you could have while maintaining roughly the same net torque would be an average of 50% current.
Knowing the supply voltage and motor resistance and inductance I can find the time it takes to reach the current limit or I could determine what current I can achieve within a shorter time period at a reduced torque. When looking at the current table in the driver datasheet and it says the percentage of the trip current to each phase I'm understanding that to mean that the driver will apply the supply voltage until the target current percentage is reached or as close to it as it can get if the on time is too short. For example under 1/16th stepping it shows 100% on phase 1 for step 1 and 2, then 98.44%, 95.31%, 92.19%. If the on time isn't long enough to reach 100% on step one then the current just looks like the exponential increasing curve. Then there would be some slow decay because the next step is increasing but on step 2 the current is already at some percentage of the trip current so it continues to try and reach it's target percentage.
I've taken the data from the current table and plotted the points which resemble sine and cosine waves but mathematically they don't match so I'm not sure how the manufacturer came up with those specific current percentage values. I also tried computing the values from a sine and cosine function and then computed their values +/- 5% which is the deviance given in the spec sheet. The values fall within those ranges from the real sine and cosine functions but with no specific pattern. I also noticed that when I did a regression fit to the datasheet values, a 6th order polynomial fit almost perfectly, much better than sine or cosine so I'm thinking that maybe they used a polynomial approximation because it is easier to calculate than sine and cosine.
I guess part of what's not making sense with this is that the net torque varies quite a bit in between full steps which I would have expected the phase currents to produce a relatively constant net torque but vary the ratio between the 2 phases. If at each full step each phase is run at 70.31% of the trip current then why do the micro steps not also average 70.31% over the 2 phases? Obviously if a phase can only go to 100% of it's trip current and each phase cycles between 0-100% then the most you could have while maintaining roughly the same net torque would be an average of 50% current.