Why do my steering wheel shake really fast right to left after installing a rack and pinion and power steering pump?

steering rack or gear . 2X2 - 4X4 engine . Depends on steering system .
When you turn the steering wheel, the steering gear rotates the pitman arm which forces the relay rod to one side. The tie rods connect to the relay rod with the ball studs. The tie rods transfer the steering force to the wheels. Use the tie rods in toe adjustments. The tie rods are adjustable. The pitman arm support the relay rod. The idler arm pivots on a support attached to the frame rail and the ball stud attaches to the relay rod.
The 2 tie rod are threaded into the tube and secured with jam nuts. Right and left hand threads are used in order to permit the adjustment of toe.

Binding linkage , steering gear worn etc....

Power Steering System Description and Operation (w/o Electro-Hydraulic Steering)
The hydraulic power steering pump is a constant displacement vane-type pump that provides hydraulic pressure and flow for the power steering gear. The hydraulic power steering pumps are either belt-driven or direct-drive, cam-driven.
The power steering fluid reservoir holds the power steering fluid and may be integral with the power steering pump or remotely located. The following locations are typical locations for the remote reservoir:
• Mounted to the front of the dash panel
• Mounted to the inner fender
• Mounted to a bracket on the engine
The 2 basic types of power steering gears are listed below:
• A recirculating ball system
• A rack and pinion system
In the recirculating ball system, a worm gear converts steering wheel movement to movement of a sector shaft. A pitman arm attached to the bottom of the sector shaft actually moves one tie rod and an intermediate rod move the other tie rod.
In the rack and pinion system, the rack and the pinion are the 2 components that convert steering wheel rotation to lateral movement. The steering shaft is attached to the pinion in the steering gear. The pinion rotates with the steering wheel. Gear teeth on the pinion mesh with the gear teeth on the rack. The rotating pinion moves the rack from side to side. The lateral action of the rack pushes and pulls the tie rods in order to change the direction of the vehicle's front wheels.
The power steering pressure hose connects the power steering pump union fitting to the power steering gear and allows pressurized power steering fluid to flow from the pump to the gear.
The power steering return hose returns fluid from the power steering gear back to the power steering fluid reservoir. The power steering return line may contain an integral fin-type or line-type power steering fluid cooler.
In a typical power steering system, a pump generates hydraulic pressure, causing fluid to flow, via the pressure hose, to the steering gear valve assembly. The steering gear valve assembly regulates the incoming fluid to the right and left chambers in order to assist in right and left turns.
Turning the steering wheel activates the valve assembly, which applies greater fluid pressure and flow to 1 side of the steering gear piston, and lower pressure and flow to the other side of the piston. The pressure assists the movement of the gear piston. Tie rods transfer this force to the front wheels, which turn the vehicle right or left.


Your best bet , take it to a qualified repair shop.

Here you are - power rack & pinion.

Except 2.2L and 1993-96 3.1L Engines
See Figure 1

1. Raise the intermediate shaft seal and remove intermediate shaft-to-stub shaft pinch bolt.
2. Remove the air cleaner and disconnect the pressure hoses from the steering gear.
3. Raise and support the vehicle on jackstands, then remove both front wheel and tire assemblies.
4. Remove the cotter pins and nuts from both tie rod ends. Using tool J-6627 or BT-7101, press the tie rod ends from the steering knuckle.
5. If equipped with an Air Management pipe, remove the bracket bolt from the crossmember.
6. Remove the 2 rear cradle mounting bolts and lower the rear of the cradle about 4-5 in. (102-127mm).

WARNING
If the rear of the cradle is lowered too far, the engine components nearest the cowl may be damaged.

1. If equipped, remove the rack and pinion heat shield.

Fig. Fig. 1: Power rack and pinion assembly

1. Remove the rack and pinion mounting bolts, then the gear assembly through the left wheel opening.

To install:

1. Install the gear assembly through the left wheel opening and install the mounting bolts.
2. Install the heat shield.
3. Raise the rear of the cradle and install the mounting bolts.
4. Install the bracket bolt to the crossmember under the air management pipe.
5. Install the tie rod ends to the steering knuckles, install the retaining nuts and insert new cotter pins.
6. Install the front wheels and lower the vehicle.
7. Install the high pressure hoses to the steering gear and install the air cleaner.
8. Install the intermediate shaft seal and the intermediate shaft-to-stub shaft pinch bolt.

2.2L Engine

1. Disconnect the negative battery cable.
2. Install an engine support fixture J-28467-A, or the equivalent.
3. Raise and safely support the vehicle.
4. Remove the tire and wheel assembly.
5. Remove the intermediate shaft lower pinch bolt.
6. Disconnect the intermediate shaft from stub shaft.

CAUTION
Failure to disconnect the intermediate shaft from the rack and pinion stub shaft can result in damage to the steering gear and/or intermediate shaft. This damage can cause loss of steering control which could result in personal injury.

1. Remove the exhaust pipe hanger bracket near rear of frame including the brake line retainer and rubber exhaust pipe hangers.
2. Remove the engine and transaxle mount nuts at the subframe.
3. Support the rear of the subframe with jack stands.
4. Remove the rear subframe bolts and discard.
5. Lower the subframe for access to rack and pinion.

Do not lower the rear of the cradle too far, as damage to engine components nearest the cowl may result.

1. Remove the cotter pins and castle nuts from the outer tie rod ends and separate the tie rod ends from the steering knuckles using a suitable puller.
2. Disconnect the power steering lines from the steering gear.
3. Remove the rack and pinion mounting bolts and nuts.
4. Remove the rack and pinion through left wheel opening.

To Install:

1. Install the rack and pinion through left wheel opening.
2. Install the rack and pinion mounting bolts and nuts and tighten to 66 ft. lbs. (90 Nm).
3. Connect the power steering lines to the rack using new O-rings and tighten the fittings to 13 ft. lbs. (17 Nm) on the return line and 21 ft. lbs. (28 Nm) on the pressure line.
4. Install the power steering line clip to steering gear.
5. Connect the tie rod ends to the steering knuckles. Tighten the castle nuts to 31 ft. lbs. (42 Nm). Install new cotter pins.
6. Raise the subframe into position and install new frame mounting bolts. Tighten the bolts to 103 ft. lbs. (140 Nm).
7. Remove the jack.
8. Install the engine mount and transaxle mount nuts and tighten to 39 ft. lbs. (53 Nm).
9. Install the exhaust pipe hanger bracket near the rear of frame including brake line retainer and rubber exhaust pipe hanger.
10. Connect the intermediate shaft to the stub shaft and tighten the pinch bolt to 29 ft. lbs. (40 Nm).
11. Install the tire and wheel assembly.
12. Lower the vehicle.
13. Remove the support fixture.
14. Connect the negative battery cable.
15. Refill the power steering reservoir and bleed the system.
16. Check the front end alignment and adjust as necessary.

3.1L Engine (VIN M)

1. Disconnect the negative battery cable.
2. Remove engine torque strut from engine.
3. Install an engine support fixture J-28467-A, or the equivalent.
4. Raise and safely support the vehicle.
5. Remove the tire and wheel assembly.
6. Remove the cotter pins and castle nuts from the outer tie rod ends and separate the tie rod ends from the steering knuckles using a suitable puller.
7. Remove the center engine and rear transaxle mounts from the frame.
8. Remove the intermediate shaft lower pinch bolt.
9. Disconnect the intermediate shaft from stub shaft.

CAUTION
Failure to disconnect the intermediate shaft from the rack and pinion stub shaft can result in damage to the steering gear and/or intermediate shaft. This damage can cause loss of steering control which could result in personal injury.

1. Remove the brace bolts and brace, including brake line brace.
2. Support the rear of the subframe with jack stands.
3. Remove the rear subframe bolts and discard.
4. Lower the subframe for access to rack and pinion.
5. Remove the steering gear heat shield.
6. Remove the clip holding lines at rack assembly.
7. Disconnect the power steering lines and O-rings.
8. Remove the rack and pinion mounting bolts and nuts.
9. Remove the rack and pinion unit through the left wheel well.

To Install:

1. Install the rack and pinion through left wheel opening.
2. Install the rack and pinion mounting bolts and nuts and tighten the mounting bolts to 66 ft. lbs. (90 Nm).
3. Connect the power steering lines to the rack using new O-rings and tighten the fittings to 13 ft. lbs. (17 Nm) on the return line and 21 ft. lbs. (28 Nm). on the pressure line.
4. Install the power steering line clip to steering gear.
5. Install the steering gear heat shield.
6. Raise the subframe into position and install new frame mounting bolts. Tighten the bolts to 103 ft. lbs. (140 Nm).
7. Remove the jack.
8. Install the engine mount and transaxle mount nuts and tighten to 39 ft. lbs. (53 Nm).
9. Install the brace and bolts including brake line brace.
10. Connect the intermediate shaft to the stub shaft and tighten the pinch bolt to 29 ft. lbs. (40 Nm).
11. Connect the tie rod ends to the steering knuckles. Tighten the castle nuts to 31 ft. lbs. (42 Nm). Install new cotter pins.
12. Install the tire and wheel assembly.
13. Lower the vehicle.
14. Remove the support fixture.
15. Connect the negative battery cable.
16. Refill the power steering reservoir and bleed the system.
17. Check the front end alignment and adjust as necessary.

You aren't saying what engine is in it, or whether it is manual or power steering. Here is the R/R procedure for power steering rack for all engine sizes.

Except 2.2L and 1993-96 3.1L Engines
See Figure 1

1. Raise the intermediate shaft seal and remove intermediate shaft-to-stub shaft pinch bolt.
2. Remove the air cleaner and disconnect the pressure hoses from the steering gear.
3. Raise and support the vehicle on jackstands, then remove both front wheel and tire assemblies.
4. Remove the cotter pins and nuts from both tie rod ends. Using tool J-6627 or BT-7101, press the tie rod ends from the steering knuckle.
5. If equipped with an Air Management pipe, remove the bracket bolt from the crossmember.
6. Remove the 2 rear cradle mounting bolts and lower the rear of the cradle about 4-5 in. (102-127mm).

WARNING
If the rear of the cradle is lowered too far, the engine components nearest the cowl may be damaged.

1. If equipped, remove the rack and pinion heat shield.

Fig. Fig. 1: Power rack and pinion assembly

1. Remove the rack and pinion mounting bolts, then the gear assembly through the left wheel opening.

To install:

1. Install the gear assembly through the left wheel opening and install the mounting bolts.
2. Install the heat shield.
3. Raise the rear of the cradle and install the mounting bolts.
4. Install the bracket bolt to the crossmember under the air management pipe.
5. Install the tie rod ends to the steering knuckles, install the retaining nuts and insert new cotter pins.
6. Install the front wheels and lower the vehicle.
7. Install the high pressure hoses to the steering gear and install the air cleaner.
8. Install the intermediate shaft seal and the intermediate shaft-to-stub shaft pinch bolt.

2.2L Engine

1. Disconnect the negative battery cable.
2. Install an engine support fixture J-28467-A, or the equivalent.
3. Raise and safely support the vehicle.
4. Remove the tire and wheel assembly.
5. Remove the intermediate shaft lower pinch bolt.
6. Disconnect the intermediate shaft from stub shaft.

CAUTION
Failure to disconnect the intermediate shaft from the rack and pinion stub shaft can result in damage to the steering gear and/or intermediate shaft. This damage can cause loss of steering control which could result in personal injury.

1. Remove the exhaust pipe hanger bracket near rear of frame including the brake line retainer and rubber exhaust pipe hangers.
2. Remove the engine and transaxle mount nuts at the subframe.
3. Support the rear of the subframe with jack stands.
4. Remove the rear subframe bolts and discard.
5. Lower the subframe for access to rack and pinion.

Do not lower the rear of the cradle too far, as damage to engine components nearest the cowl may result.

1. Remove the cotter pins and castle nuts from the outer tie rod ends and separate the tie rod ends from the steering knuckles using a suitable puller.
2. Disconnect the power steering lines from the steering gear.
3. Remove the rack and pinion mounting bolts and nuts.
4. Remove the rack and pinion through left wheel opening.

To Install:

1. Install the rack and pinion through left wheel opening.
2. Install the rack and pinion mounting bolts and nuts and tighten to 66 ft. lbs. (90 Nm).
3. Connect the power steering lines to the rack using new O-rings and tighten the fittings to 13 ft. lbs. (17 Nm) on the return line and 21 ft. lbs. (28 Nm) on the pressure line.
4. Install the power steering line clip to steering gear.
5. Connect the tie rod ends to the steering knuckles. Tighten the castle nuts to 31 ft. lbs. (42 Nm). Install new cotter pins.
6. Raise the subframe into position and install new frame mounting bolts. Tighten the bolts to 103 ft. lbs. (140 Nm).
7. Remove the jack.
8. Install the engine mount and transaxle mount nuts and tighten to 39 ft. lbs. (53 Nm).
9. Install the exhaust pipe hanger bracket near the rear of frame including brake line retainer and rubber exhaust pipe hanger.
10. Connect the intermediate shaft to the stub shaft and tighten the pinch bolt to 29 ft. lbs. (40 Nm).
11. Install the tire and wheel assembly.
12. Lower the vehicle.
13. Remove the support fixture.
14. Connect the negative battery cable.
15. Refill the power steering reservoir and bleed the system.
16. Check the front end alignment and adjust as necessary.

3.1L Engine (VIN M)

1. Disconnect the negative battery cable.
2. Remove engine torque strut from engine.
3. Install an engine support fixture J-28467-A, or the equivalent.
4. Raise and safely support the vehicle.
5. Remove the tire and wheel assembly.
6. Remove the cotter pins and castle nuts from the outer tie rod ends and separate the tie rod ends from the steering knuckles using a suitable puller.
7. Remove the center engine and rear transaxle mounts from the frame.
8. Remove the intermediate shaft lower pinch bolt.
9. Disconnect the intermediate shaft from stub shaft.

CAUTION
Failure to disconnect the intermediate shaft from the rack and pinion stub shaft can result in damage to the steering gear and/or intermediate shaft. This damage can cause loss of steering control which could result in personal injury.

1. Remove the brace bolts and brace, including brake line brace.
2. Support the rear of the subframe with jack stands.
3. Remove the rear subframe bolts and discard.
4. Lower the subframe for access to rack and pinion.
5. Remove the steering gear heat shield.
6. Remove the clip holding lines at rack assembly.
7. Disconnect the power steering lines and O-rings.
8. Remove the rack and pinion mounting bolts and nuts.
9. Remove the rack and pinion unit through the left wheel well.

To Install:

1. Install the rack and pinion through left wheel opening.
2. Install the rack and pinion mounting bolts and nuts and tighten the mounting bolts to 66 ft. lbs. (90 Nm).
3. Connect the power steering lines to the rack using new O-rings and tighten the fittings to 13 ft. lbs. (17 Nm) on the return line and 21 ft. lbs. (28 Nm). on the pressure line.
4. Install the power steering line clip to steering gear.
5. Install the steering gear heat shield.
6. Raise the subframe into position and install new frame mounting bolts. Tighten the bolts to 103 ft. lbs. (140 Nm).
7. Remove the jack.
8. Install the engine mount and transaxle mount nuts and tighten to 39 ft. lbs. (53 Nm).
9. Install the brace and bolts including brake line brace.
10. Connect the intermediate shaft to the stub shaft and tighten the pinch bolt to 29 ft. lbs. (40 Nm).
11. Connect the tie rod ends to the steering knuckles. Tighten the castle nuts to 31 ft. lbs. (42 Nm). Install new cotter pins.
12. Install the tire and wheel assembly.
13. Lower the vehicle.
14. Remove the support fixture.
15. Connect the negative battery cable.
16. Refill the power steering reservoir and bleed the system.
17. Check the front end alignment and adjust as necessary.

Sounds like a bad replacement rack.. Did you buy a rebuilt rack? Look up the number for A1 Cardone.. They are in my openion the best rebuilders of rack and pinion.. You can talk to their tech team and they can answer your question.. I have never seen this problem.. i have had racks that the internal valves have went bad and lock up the rack and pump.. Post a comment here and let us know what you find so we will know too.

I would say you have a defective power steering pump since the rack is replaced. You did bleed the air out right? Raise the front wheels off the ground and slowly turn the wheels left to right and see if the air is bled out of the system. There is not "reset button"

Disconnect the column from the rack & pinion, And then see if the wheel will rotate left. If it does, then it IS the rack & pinion or some thing is jamming it. That is a classic sign of a bad rack & pinion. It takes more hydraulic pressure to turn left than to the right, and the and so the floating ball hits the seal harder, and wears it out faster. Then the pressure just returns to the pump in stead of moving the tires left.

NOTE: DO NOT turn the steering wheel more than it does when connected the the rack & pinion.
For this test one turn either way from center will suffice. If you turn it more, or fast, you will probably break the "clocking spring" inside the steering wheel. Then the air-bag warning light will come on. The spring tells the air-bag when its safe to fire the bag in relation to the wheels position.

Hope this helps.

you need to bleed the rack. you can try to turn the steering wheel to the left and hold for 5 sec and then to the right and hold, continue this a few times check fluid and repeat. you can also try to loosen line on rack and turn wheel to bleed air out then tighten before turning wheel again.

YOU HAVE TO SAFELY RAISE SUPPORT VECHICLE ON JACK STANDS.MAKE SURE YOU HAVE VECHICLE PARKED ON LEVEL SOLID GROUND.ONCE VECHICLE RAISED.REMOVE FRONT WHEELS.REMOVE TIE RODS END COTTER PINS AND CASTLE NUTS.REMOVE TIE ROD ENDS FROM THE KNUCKLES.REMOVE FRONT STABILIZER BAR.POSITION THE DASH OPENING WEATHER SEAL FOR THE STEERING COLUMN OUT OF THE WAY.REMOVE OR DISCONNECT THE FOLLOWING.REMOVE PINCH BOLT RETAINING THE STEERING COLUMN INTERMEDIATE SHAFT COUPLING.REMOVE STEERING GEAR RETAINING NUTS BOLTS.REMOVE REAR SUBFRAME BOLTS.USE WIRE TO SUPPORT EXHAUST COMPONENTS UNLESS YOU ARE REMOVING THEM COMPLETELY.SUPPORT THE EXHAUST SYSTEM FLEX TUBE AND REMOVE THE FLEX TUBE TO DUAL CONVERTER Y PIPE ATTACHMENT.LOWER THE VECHICLE SLIGHTLY UNTIL THE REAR SUBFRAME SEPARATES FROM THE BODY APPROXIMATELY 4 INCHES.REMOVE THE HEAT SHIELD BAND AND FOLD THE HEAT SHIELD DOWN.ROTATE THE RACK AND PINION ASSEMBLY TO CLEAR THE BOLTS FROM THE FRONT SUBFRAME AND PULL TOWARD THE DRIVERS SIDE OF THE VECHICLE.PLACE A DRAIN PAN UNDER THE VECHICLE AND DISCONNECT THE POWER STEERING LINES.REMOVE THE RACK AND PINION ASSEMBLY THROUGH THE DRIVERS SIDE OF THE VECHICLE***** TO INSTALL ****** INSTALL NEW TEFLON O - RINGS ON THE POWER STEERING LINE FITTINGS. PLACE THE RACK AND PINION RETAINING BOLTS IN THE GEAR HOUSING.INSTALL RACK AND PINION ASSEMBLY THROUGH THE DRIVERS SIDE OF THE VECHICLE.INSTALL POWER STEERING LINES ON THE RACK AND PINION ASSEMBLY. INSTALL RACK AND PINION ASSEMBLY ON THE SUBFRAME.INSTALL ******** HEAT SHIELD.INSTALL TIE ROD ENDS TO THE KNUCKLES TIGHTEN THE CASTLE NUTS AND INSTALL THE COTTER PINS.INSTALL STABILIZER BAR.INSTALL RACK AND PINION ASSEMBLY RETAINING BOLTS.TORQUE THEM TO 85 - 99 FT LBS. RAISE VECHICLE UNTIL SUBFRAME CONTACTS THE BODY.INSTALL REAR SUBFRAME RETAINING BOLTS TORQUE THEM TO 83 - 112 FT LBS.INSTALL EXHAUST SYSTEM FLEX TUBE TO DUAL CONVERTER Y PIPE.INSTALL FRONT WHEELS.INSTALL A NEW PINCH BOLT IN THE STEERING COLUMN INTERMEDIATE SHAFT COUPLING ON THE RACK INPUT SHAFT TORQUE PINCH BOLT TO 25 - 33 FT LBS.POSITION THE STEERING COLUMN OPENING WEATHER SEAL OVER THE STEERING GEAR HOUSING.LOWER THE VECHICLE FILL THE POWER STEERING FLUID RESERVOIR. START THE VECHICLE AND CHECK FOR LEAKS. CHECK FOR PROPER WHEEL ALIGNMENT AND STEERING WHEEL POSITION.BLEED POWER STEERING SYSTEM.

check the power steering pump, if its good than it will be rack and pinion issue. the pump create a high pressure to help assist with steering, and the rack and pinion work like hydraulic cylinder which receive the pressure from the pump and the steering work like control valves. by turn left or right you controling the pressure to make the wheels turn either right or left. check and see if you have any leaks.

To find out witch it is,pump or rack and pinion,break loose the presure line on the power steering pump with a wench.Start the car and turn the steering wheel back and forth,you may need to loosen the nut on the power steering hose two or three turns to get the fluid to shoot out.It should come out pretty forceful.If it doesn`t,then replace the pump.If it does come out really powerful,replace the rack and pinion.