## Planetary Roller Screw Selection Process

The data on the following pages is designed to assist you in selecting the proper screw size for your application. Please contact our Sales Engineering department for assistance, if required.Basic Dynamic Load Ratings (C):Dynamic load is used to calculate the fatigue life of a planetary roller screw. The dynamic load rating is defined as load, constant in magnitude and direction under which 90% of a statistically significant number of apparently identical planetary roller screws reach an operating life of revolutions (L10).Static Load Ratings (C0):Static Load rating (C0) is a load that causes permanent deformation at the most heavily loaded contact equal to .0001 of the curvature diameter of the rolling element.Static Load Safety Factors (S0):In order to prevent deformations that could impair the proper function and the operating noise of the planetary roller screw, a safety factor (S0) should be used when selecting a roller screw based on basis of its static load rating. For operations with quasi-static load applications (such as presses) where load occurs primarily on the same portion of the stroke, it is recommended to use a higher S0.Theoretical Life:Theoretical life (L10 or Lh) is the operating time reached by 90% of a group of apparently identical planetary roller screws operating under the same conditions. Theoretical life is calculated as:[

L_1_0 = (frac{C} {F_m})^3 or C_r_e_g= F_m .(L_1_0) ^frac{1}{3}

]Where: = Life(millions of shaft revolutions)*= Dynamic load capacity (kN)** = Cubic mean load (kN)** = Required dynamic load capcity (kN)*Theoretical life, normally expressed in 106 revolutions, can be expressed in different operating units such as hours:[

L_h = frac{10^6.(frac{C}{F_m})} {n_e_q .60}

]Where: = Life(hrs)*= Screw equivalent rotational speed(rpm)*Equivalent Load:Operating Loads can be quantified by the incremental load and stroke characteristics that the system is subject to: masses, inertia, etc. For systems with varying conditions (changes of load magnitude, duration, and/or speed), a more complex calculation would be required. Please contact CMC sales engineering for more information on these types of applications. The equivalent load is the calculated cubic mean operating load used for determining life. This is dependent on load pattern.Equivalent cubic mean load can be calculated as:[F_m=frac{ (F_1^3 L_1 + F_2^3 L_2 + F_3^3 L_3 + …)^frac{1}{3} }{(L_1 + L_2 + L_3 +…)^frac{1}{3}}]Where: = Incremental force components of

stroke(kN)*= Incremental stroke components associatedwith each load(mm)*Rigidity of Roller Screw:The rigidity of a roller screw assembly is a function of many parameters, including: nut rigidity, bearing support rigidity, screw shaft rigidity, mounting housing rigidity, and mounting arrangement. If known, all these parameters can be assembled in a formula as follows:

[C_a = (frac{1 }{C_s} + frac{1 }{C_n} + frac{1 }{C_b} + frac{1 }{C_h})^-^1]Where (rigidity in ….. ) = Total system rigidity = Screw shaft rigidity = Nut rigidity = Housing rigidity

**The screw rigidity can be calculated as:**[C_s = 165.d_0 . f_e] = Rigidity of the screw = Screw pitch diameter (mm) = Shaft stiffness factor

**The nut rigidity can be calculated as follows:**[C_n = f_n . ( F_a_x)^frac{1}{3}] = Applied load (N) = Nut stiffness factor (provided on request)

Column Strength:If the screw is subjected to compressive loads, a verification of its suitability to the loading conditions must be evaluated. The buckling capacity of the screw can be evaluat-ed as follows:[F_c= frac{34.f_3.d_2^4.10^3 }{L^2 }]Where: = Buckling strength (N) = Shaft stiffness factor dependent on end condition (see table) = Screw shaft root diameter (mm) = Free length (distance between support bearings)

Critical Speed:

Diameter and free length of the screw

The critical speed of the screw shaft is calculated as follows:[n_c_r = frac{f_1 . d_1 . 10^7 }{ L^2}]Where: = Critical speed of screw shaft ( n o safety factor) (rpm) = End support stiffness factor = Screw outside diameter (mm)

Efficiency and Driving Torque:The efficiency of a planetary roller screw is dependent on its operating parameters. The friction of the system is ependent on many factors that can vary. The following calculation is a simplification of the screw selection process that can change based on variables.[eta = frac{1}{1 + frac{pi . d_0}{P_h}mu}][eta^1 = 2 – frac{1}{eta}][eta_p = eta . 0.9]Where:

= Theoretical direct efficiency: converting shaft rotation into axial motion

= Theoretical indirect efficiency (backdriving)

= Practical efficiency: the value of 0.9 should be used as an average value between the practical efficiency of a new screw and that of a normally run screw.This is the value that should be used for all industry applications in all normal working conditions.

= Lead of screw (mm)

= Pitch diameter of screw (mm)

= Coefficient of frictionTorque Required:To move an axial load at constant speed the screw requires a motor torque and its magnitude can be calculated as:[T= frac{F . P_h }{2 . pi . eta_P . 10^3}]Where: = Required input torque (* Nm*) = Axial load developed by screw (* N*)To restrain an axial load, the screw must be equipped with a brake. The restraining torque is calculated as:[T_B = frac{F . P_h . eta_1}{2. pi . 10^3}]Where: = Required braking torque (* Nm*)NOTE: Start-up torque will be greater than the value .

## Lubrication

As a general rule, the same lubricants are used for planetary roller screws as for rolling element bearings are either oil or grease. The type of lubricant used is most dependent on the operating and maintenance conditions.Lubrication:Proper lubrication is essential to the proper functioning of a roller screw. The key point is in the initial lubrication of the nut so that all components have adequate lubrication.Unless otherwise specified, CMC roller screws are shipped “dry” with only a protective coating, and the customer must properly lubricate the roller screw before usage.The volume, spread, and frequency of re-application of the lubricant must be properly selected and monitored. At high speed the lubricant on the surface of the shaft may be thrown off by centrifugal forces. Therefore, it is important to monitor this effect when operating at high speed, and considering this when selecting a lubricant.Monitoring the equilibrium temperature reached by the nut permits the frequency of relubrication or oil flow rates to be optimized.The selection of lubricant and the maintenance of relubrication is the responsibility of the customer.Oil Lubrication:A centralized recirculating oil system is ideal due to its ability to continually supply filtered, temperature controlled oil at prescribed flow rates. While such systems represent the optimum, they are not always practical from a cost or size perspective and alternate solutions are available that can achieve effective results if properly configured.Selection of Oil:Circulating mineral oils with EP additives to enhance resistance to aging and corrosion in compliance with DIN 51517, Part 2, are particularly suitable for the lubrication of planetary roller screws. Operating speed, ambient temperature and operating temperature are all factors in determining the required viscosity of the lubricant.The required volume of oil depends on the screw diameter, the number of supporting rollers and the amount of heat to dissipate.For immersion lubrication, the oil level should be such that the lowest roller is completely submerged in oil. The amount of oil and the change interval depend on the intensity of the loading on the system and the details of the installation.Figure A below shows the operating viscosity, νk (mm²/s), required for any given mean speed of the screw system based on the diameter of the shaft. The viscosity, νk, prescribed by figure A, ensures a sufficient lubrication to achieve the nominal life for the system, provided that the lubricant is properly filtered and maintained. Intermediate values can be estimated by interpolation between the curves provided in figure A.

Figure A

Figure B

Nominal lubricant viscosity can be determined based on the required viscosity, νk, the steady state temperature of the roller screw using the viscosity-temperature diagram in figure B, and the operating temperature of the roller screw system. Nominal viscosity is the viscosity of the lubricant at 40°C. Viscosity classes consistent with ISO VG (DIN 51517), Part 2, are plotted in figure B. The operating temperature of the roller screw must be known or estimated to calculate the required nominal viscosity using this technique.Grease Lubrication:Grease is the most common form of lubrication for CMC roller screws, and provides an effective solution for most applications. The required viscosity in the case of grease lubrication can be calculated using the same process outlined above for oil viscosity determination. The viscosity of grease is rated with ISO VG levels just as oils and this information is typically provided by grease manufacturers. Re-greasing intervals depend on the screw arrangement, size and operating conditions.

## Planetary Roller Screw Installation and Maintenance

Roller screw systems require little maintenance when compared to fluid power alternatives, such as hydraulic and pneumatic systems.StorageRoller screws are precision components and should be handled with care. Roller screws should be allowed to remain in their shipping crate or properly supported when stored.CMC roller screws are shipped in sealed plastic, and the units should remain sealed until they are installed for use.Disassembly/Re-assemblyIn some cases, the roller nut must be removed and re-installed on the shaft. In such cases, CMC can provide a custom fit mandrel to ensure that internal integrity of the roller screw assembly is maintained at all times during the assembly and disassembly process.Screw Shaft End DesignStructural integrity of custom end features of the shaft designed per the customer’s specifications are the responsibility of the customer.Starting up the ScrewAfter the assembly has been cleaned, mounted, and lubricated, it is recommended that the nut makes several full strokes at low speed. This allows installation and verification of limit switches or any other mechanism unique to the assembly prior to applying full load and operating at full speed.Operating TemperatureScrews made from standard steels and operating under normal loads can sustain temperature ranges from –20 degrees Celsius (-4 degrees Fahrenheit) to +110 degrees Celsius (230 degrees Fahrenheit). If your screw will be operating outside of these temperature ranges, contact CMC.

## Planetary Roller Screw Selection Process

The data on the following pages is designed to assist you in selecting the proper screw size for your application. Please contact our Sales Engineering department for assistance, if required.

#### Basic Dynamic Load Ratings (C):

Dynamic load is used to calculate the fatigue life of a planetary roller screw. The dynamic load rating is defined as load, constant in magnitude and direction under which 90% of a statistically significant number of apparently identical planetary roller screws reach an operating life of revolutions (L10).

#### Static Load Ratings (C0):

Static Load rating (C0) is a load that causes permanent deformation at the most heavily loaded contact equal to .0001 of the curvature diameter of the rolling element.

#### Static Load Safety Factors (S0):

In order to prevent deformations that could impair the proper function and the operating noise of the planetary roller screw, a safety factor (S0) should be used when selecting a roller screw based on basis of its static load rating. For operations with quasi-static load applications (such as presses) where load occurs primarily on the same portion of the stroke, it is recommended to use a higher S0.

#### Theoretical Life:

Theoretical life (L10 or Lh) is the operating time reached by 90% of a group of apparently identical planetary roller screws operating under the same conditions. Theoretical life is calculated as:

[

L_1_0 = (frac{C} {F_m})^3 or C_r_e_g= F_m .(L_1_0) ^frac{1}{3}

]

Where:

= Life(millions of shaft revolutions)

*= Dynamic load capacity (kN)*

* = Cubic mean load (kN)*

* = Required dynamic load capcity (kN)*

Theoretical life, normally expressed in 106 revolutions, can be expressed in different operating units such as hours:

[

L_h = frac{10^6.(frac{C}{F_m})} {n_e_q .60}

]

Where:

= Life(hrs)

*= Screw equivalent rotational speed(rpm)*

#### Equivalent Load:

Operating Loads can be quantified by the incremental load and stroke characteristics that the system is subject to: masses, inertia, etc. For systems with varying conditions (changes of load magnitude, duration, and/or speed), a more complex calculation would be required. Please contact CMC sales engineering for more information on these types of applications. The equivalent load is the calculated cubic mean operating load used for determining life. This is dependent on load pattern.

Equivalent cubic mean load can be calculated as:

[

F_m=frac{ (F_1^3 L_1 + F_2^3 L_2 + F_3^3 L_3 + …)^frac{1}{3} }{(L_1 + L_2 + L_3 +…)^frac{1}{3}}

]

Where:

= Incremental force components of

stroke(kN)

*= Incremental stroke components associated
with each load(mm)*

#### Rigidity of Roller Screw:

The rigidity of a roller screw assembly is a function of many parameters, including: nut rigidity, bearing support rigidity, screw shaft rigidity, mounting housing rigidity, and mounting arrangement. If known, all these parameters can be assembled in a formula as follows:

[

C_a = (frac{1 }{C_s} + frac{1 }{C_n} + frac{1 }{C_b} + frac{1 }{C_h})^-^1

]

Where (rigidity in ….. )

= Total system rigidity

= Screw shaft rigidity

= Nut rigidity

= Housing rigidity

**Rigidity Fe Factor**

**The screw rigidity can be calculated as:**

[

C_s = 165.d_0 . f_e

]

= Rigidity of the screw

= Screw pitch diameter (mm)

= Shaft stiffness factor

**The nut rigidity can be calculated as follows:**

[

C_n = f_n . ( F_a_x)^frac{1}{3}

]

= Applied load (N)

= Nut stiffness factor (provided on request)

#### Column Strength:

If the screw is subjected to compressive loads, a verification of its suitability to the loading conditions must be evaluated. The buckling capacity of the screw can be evaluat-ed as follows:

[

F_c= frac{34.f_3.d_2^4.10^3 }{L^2 }

]

Where:

= Buckling strength (N)

= Shaft stiffness factor dependent on end condition (see table)

= Screw shaft root diameter (mm)

= Free length (distance between support bearings)

#### Critical Speed:

- The maximum achievable rotational velocity of a CMC roller screw is affected by these parameters:

Diameter and free length of the screw - End support configuration
- Rotational Speed capability
- Rotating component (nut or screw)

The critical speed of the screw shaft is calculated as follows:

[

n_c_r = frac{f_1 . d_1 . 10^7 }{ L^2}

]

Where:

= Critical speed of screw shaft ( n o safety factor) (rpm)

= End support stiffness factor

= Screw outside diameter (mm)

#### Efficiency and Driving Torque:

The efficiency of a planetary roller screw is dependent on its operating parameters. The friction of the system is ependent on many factors that can vary. The following calculation is a simplification of the screw selection process that can change based on variables.

[

eta = frac{1}{1 + frac{pi . d_0}{P_h}mu}

]

[

eta^1 = 2 – frac{1}{eta}

]

[

eta_p = eta . 0.9

]

Where:

= Theoretical direct efficiency: converting shaft rotation into axial motion

= Theoretical indirect efficiency (backdriving)

= Practical efficiency: the value of 0.9 should be used as an average value between the practical efficiency of a new screw and that of a normally run screw.

This is the value that should be used for all industry applications in all normal working conditions.

= Lead of screw (mm)

= Pitch diameter of screw (mm)

= Coefficient of friction

#### Torque Required:

To move an axial load at constant speed the screw requires a motor torque and its magnitude can be calculated as:

[

T= frac{F . P_h }{2 . pi . eta_P . 10^3}

]

Where:

= Required input torque (* Nm*)

= Axial load developed by screw (* N*)

To restrain an axial load, the screw must be equipped with a brake. The restraining torque is calculated as:

[

T_B = frac{F . P_h . eta_1}{2. pi . 10^3}

]

Where:

= Required braking torque (* Nm*)

NOTE: Start-up torque will be greater than the value .

## Lubrication

As a general rule, the same lubricants are used for planetary roller screws as for rolling element bearings are either oil or grease. The type of lubricant used is most dependent on the operating and maintenance conditions.

#### Lubrication:

Proper lubrication is essential to the proper functioning of a roller screw. The key point is in the initial lubrication of the nut so that all components have adequate lubrication.

Unless otherwise specified, CMC roller screws are shipped “dry” with only a protective coating, and the customer must properly lubricate the roller screw before usage.

The volume, spread, and frequency of re-application of the lubricant must be properly selected and monitored. At high speed the lubricant on the surface of the shaft may be thrown off by centrifugal forces. Therefore, it is important to monitor this effect when operating at high speed, and considering this when selecting a lubricant.

Monitoring the equilibrium temperature reached by the nut permits the frequency of relubrication or oil flow rates to be optimized.

The selection of lubricant and the maintenance of relubrication is the responsibility of the customer.

#### Oil Lubrication:

A centralized recirculating oil system is ideal due to its ability to continually supply filtered, temperature controlled oil at prescribed flow rates. While such systems represent the optimum, they are not always practical from a cost or size perspective and alternate solutions are available that can achieve effective results if properly configured.

#### Selection of Oil:

Circulating mineral oils with EP additives to enhance resistance to aging and corrosion in compliance with DIN 51517, Part 2, are particularly suitable for the lubrication of planetary roller screws. Operating speed, ambient temperature and operating temperature are all factors in determining the required viscosity of the lubricant.

The required volume of oil depends on the screw diameter, the number of supporting rollers and the amount of heat to dissipate.

For immersion lubrication, the oil level should be such that the lowest roller is completely submerged in oil. The amount of oil and the change interval depend on the intensity of the loading on the system and the details of the installation.

Figure A below shows the operating viscosity, νk (mm²/s), required for any given mean speed of the screw system based on the diameter of the shaft. The viscosity, νk, prescribed by figure A, ensures a sufficient lubrication to achieve the nominal life for the system, provided that the lubricant is properly filtered and maintained. Intermediate values can be estimated by interpolation between the curves provided in figure A.

Figure A

Figure B

Nominal lubricant viscosity can be determined based on the required viscosity, νk, the steady state temperature of the roller screw using the viscosity-temperature diagram in figure B, and the operating temperature of the roller screw system. Nominal viscosity is the viscosity of the lubricant at 40°C. Viscosity classes consistent with ISO VG (DIN 51517), Part 2, are plotted in figure B. The operating temperature of the roller screw must be known or estimated to calculate the required nominal viscosity using this technique.

#### Grease Lubrication:

Grease is the most common form of lubrication for CMC roller screws, and provides an effective solution for most applications. The required viscosity in the case of grease lubrication can be calculated using the same process outlined above for oil viscosity determination. The viscosity of grease is rated with ISO VG levels just as oils and this information is typically provided by grease manufacturers. Re-greasing intervals depend on the screw arrangement, size and operating conditions.

## Planetary Roller Screw Installation and Maintenance

Roller screw systems require little maintenance when compared to fluid power alternatives, such as hydraulic and pneumatic systems.

#### Storage

Roller screws are precision components and should be handled with care. Roller screws should be allowed to remain in their shipping crate or properly supported when stored.

CMC roller screws are shipped in sealed plastic, and the units should remain sealed until they are installed for use.

#### Disassembly/Re-assembly

In some cases, the roller nut must be removed and re-installed on the shaft. In such cases, CMC can provide a custom fit mandrel to ensure that internal integrity of the roller screw assembly is maintained at all times during the assembly and disassembly process.

#### Screw Shaft End Design

Structural integrity of custom end features of the shaft designed per the customer’s specifications are the responsibility of the customer.

#### Starting up the Screw

After the assembly has been cleaned, mounted, and lubricated, it is recommended that the nut makes several full strokes at low speed. This allows installation and verification of limit switches or any other mechanism unique to the assembly prior to applying full load and operating at full speed.

#### Operating Temperature

Screws made from standard steels and operating under normal loads can sustain temperature ranges from –20 degrees Celsius (-4 degrees Fahrenheit) to +110 degrees Celsius (230 degrees Fahrenheit). If your screw will be operating outside of these temperature ranges, contact CMC.