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The following might seem obvious, but it shouldn't be overlooked either.

Unless you have one of those Wire EDM cutting machines, with very precise tolerances, that can seamlessly cut a shape out of blocks of metal that then, seemingly, glide out of the surrounding block, with little to no stiction¹, then your printed surfaces of the screw will have imperfections that may cause the binding. The first step would be to shave, sand and smooth the surfaces. Maybe even treat with another chemical, such as acetone (depending upon your printing material) to smooth the surfaces even further.

However, in addition to that, some lubricant may be in order. Every gear box or mechanism contains a little oil or grease.

So, your original design may still work, with a little help from smoothing and lubricating any mating surfaces. As Trish states, your design has a lot of surface friction, so every bit of polishing of the surfaces will help.

¹ Such as the objects shown at the start of this video: How these impossibly thin cuts are made

The following might seem obvious, but it shouldn't be overlooked either.

Unless you have one of those Wire EDM cutting machines, with very precise tolerances¹, that can seamlessly cut a shape out of blocks of metal that then, seemingly, glide out of the surrounding block, with little to no stiction², then your printed surfaces of the screw will have imperfections that may cause the binding. The first step would be to shave, sand and smooth the surfaces. Maybe even treat with another chemical, such as acetone (depending upon your printing material) to smooth the surfaces even further.

However, in addition to that, some lubricant may be in order. Every gear box or mechanism contains a little oil or grease.

So, your original design may still work, with a little help from smoothing and lubricating any mating surfaces. As Trish states, your design has a lot of surface friction, so every bit of polishing of the surfaces will help.

¹ Approaching $\frac{5}{1000}$ (i.e. five thousandths) of a millimetre

² Such as the objects shown at the start of this video: How these impossibly thin cuts are made

The following might seem obvious, but it shouldn't be overlooked either.

Unless you have one of those cutting machines, with very precise tolerances, that can seamlessly cut a shape out of blocks of metal that then, seemingly, glide out of the surrounding block, with little to no stiction¹, then your printed surfaces of the screw will have imperfections that may cause the binding. The first step would be to shave, sand and smooth the surfaces. Maybe even treat with another chemical, such as acetone (depending upon your printing material) to smooth the surfaces even further.

However, in addition to that, some lubricant may be in order. Every gear box or mechanism contains a little oil or grease.

So, your original design may still work, with a little help from smoothing and lubricating any mating surfaces. As Trish states, your design has a lot of surface friction, so every bit of polishing of the surfaces will help.

¹ I had recently seen such an example on YouTube, and had hoped to include a link and/or screenshot, as an illustration, but I can't find it again.

The following might seem obvious, but it shouldn't be overlooked either.

Unless you have one of those Wire EDM cutting machines, with very precise tolerances, that can seamlessly cut a shape out of blocks of metal that then, seemingly, glide out of the surrounding block, with little to no stiction¹, then your printed surfaces of the screw will have imperfections that may cause the binding. The first step would be to shave, sand and smooth the surfaces. Maybe even treat with another chemical, such as acetone (depending upon your printing material) to smooth the surfaces even further.

However, in addition to that, some lubricant may be in order. Every gear box or mechanism contains a little oil or grease.

So, your original design may still work, with a little help from smoothing and lubricating any mating surfaces. As Trish states, your design has a lot of surface friction, so every bit of polishing of the surfaces will help.

¹ Such as the objects shown at the start of this video: How these impossibly thin cuts are made

The following might seem obvious, but it shouldn't be overlooked either.

Unless you have one of those cutting machines, with very precise tolerances, that can seamlessly cut a shape out of blocks of metal that then, seemingly, glide out of the surrounding block, with little to no friction¹, then your printed surfaces of the screw will have imperfections that may cause the binding. The first step would be to shave, sand and smooth the surfaces. Maybe even treat with another chemical, such as acetone (depending upon your printing material) to smooth the surfaces even further.

However, in addition to that, some lubricant may be in order. Every gear box or mechanism contains a little oil or grease.

So, your original design may still work, with a little help from smoothing and lubricating any mating surfaces. As Trish states, your design has a lot of surface friction, so every bit of polishing of the surfaces will help.

¹ I had recently seen such an example on YouTube, and had hoped to include a link and/or screenshot, as an illustration, but I can't find it again.

The following might seem obvious, but it shouldn't be overlooked either.

Unless you have one of those cutting machines, with very precise tolerances, that can seamlessly cut a shape out of blocks of metal that then, seemingly, glide out of the surrounding block, with little to no stiction¹, then your printed surfaces of the screw will have imperfections that may cause the binding. The first step would be to shave, sand and smooth the surfaces. Maybe even treat with another chemical, such as acetone (depending upon your printing material) to smooth the surfaces even further.

However, in addition to that, some lubricant may be in order. Every gear box or mechanism contains a little oil or grease.

So, your original design may still work, with a little help from smoothing and lubricating any mating surfaces. As Trish states, your design has a lot of surface friction, so every bit of polishing of the surfaces will help.

¹ I had recently seen such an example on YouTube, and had hoped to include a link and/or screenshot, as an illustration, but I can't find it again.