Implementing Risk Responses do not in and of themselves necessarily require a change request. However, you are buying or leasing another machine then that may require a change request, per the PMBOK, pg. 358, to update:
* Resource management plan. Described in Section 9.1.3.1. The resource management plan is updated to reflect actual experience in managing project resources.
* Physical resource assignments. Described in Section 9.3.3.1. Physical resource assignments are dynamic and subject to change due to availability, the project, organization, environment, or other factors.
* Resource breakdown structure. Described in Section 9.2.3.3. Changes to the resource breakdown structure may be required to reflect the way project resources are being used.
As per the second part, if the price of your equipment is higher than anticipated AND greater than your contingency reserves, you can use management reserves which would require a change request to update the project cost baseline.