Sigma 70-200 2.8 lens has stoped autofocusing

Sounds like the autofocus motor is having issues, I'd suggest contacting Sigma.

The Nikon D40 does not have an autofocus motor, relying on the lens having one. This Sigma lens does not have such a motor, relying on the camera having one. Nikon designates lenses with an autofocus motor AF-S, Sigma calls theirs HSM.

If those lenses have a Nikon mount then they will fit on the D3000 and D3100. However, the D3000 and D3100 lack a focus motor. If the lens does not have the focus motor then you will not have the autofocus capability. Sigma calls their focus motor the HSM; if the lens does not specify HSM then they do not have the motor.

The autofocus motors in Sigma lenses that are not HSM tend to be noisy, but I presume yours is now more noisy than usual. With that, and not focusing properly, considered together, It seems to me the motor has failed or the lens parts have partially seized causing the motor to "struggle" to focus parts that are not moving as they should. I.e., once focused the motor will stop, but if the electronics are telling the motor the lens is not if focus, it will continue to try to achieve focus. Most likely, time for repair, and if in warranty, contact Sigma repair via Sigmaphoto.com.

The Sigma 70-300mm f/4-5.6 DG will not autofocus with the D40 since the lens does not feature an internal focusing motor (HSM). The D40 does not have an AF motor in the body and hence it can autofocus only with lenses featuring an integrated motor (eg. Nikon AF-S lenses, Sigma HSM lenses, Tokina DX II series etc). Unfortunately you can use the said lens only in MF mode.

Hi is the manual focus working from inf to close focus and not stoping then it needs a new hsm motor

if the motor is running but the focus is not moving the scale ring may be damage it will need to go to sigma uk

Your 28-90 AF-D lens can't autofocus with the D40, which requires AF-S lenses with a focus motor in the lens. Sigma lenses with "HSM" (HyperSonic Motor) in the name also have the focus motor.

This lens is NOT compatible as the body doesn't have a motor . £200 wasted

It is likely that the lens will need parts. Sigma is not the best for repair parts. Typically, the small nylon gears that control the AF break. It is still a useful piece in manual focus. Repair costs would likely exceed its value.